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Numerical method for solving physical or engineering problems
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical
Finite_element_method
extended finite element method (XFEM), is a numerical technique based on the generalized finite element method (GFEM) and the partition of unity method (PUM)
Extended finite element method
Extended_finite_element_method
Class of numerical techniques
common approaches to the numerical solution of PDE, along with finite element methods. For a n-times differentiable function, by Taylor's theorem the
Finite_difference_method
Class of numerical simulation algorithms
Smoothed finite element methods (S-FEM) are a particular class of numerical simulation algorithms for the simulation of physical phenomena. It was developed
Smoothed finite element method
Smoothed_finite_element_method
Numerical method used in structural mechanics
The finite element method (FEM) is a powerful technique originally developed for the numerical solution of complex problems in structural mechanics, and
Finite element method in structural mechanics
Finite_element_method_in_structural_mechanics
Method of solving linear partial differential equations
and mathematical modeling. It is similar to the more widely used finite element method, in that it breaks down the object of study into a series of points
Boundary_element_method
Branch of numerical analysis
nonconforming finite element, mixed finite element, mimetic finite difference...) inherit these convergence properties. The finite-volume method is a numerical
Numerical methods for partial differential equations
Numerical_methods_for_partial_differential_equations
This is a list of notable software packages that implement the finite element method for solving partial differential equations. This table is contributed
List of finite element software packages
List_of_finite_element_software_packages
In numerical analysis, a mixed finite element method, is a variant of the finite element method in which extra fields to be solved are introduced during
Mixed_finite_element_method
Structural analysis technique; implementation of the finite element method
method is the most common implementation of the finite element method (FEM). In applying the method, the system must be modeled as a set of simpler,
Direct_stiffness_method
In numerical analysis, the interval finite element method (interval FEM) is a finite element method that uses interval parameters. Interval FEM can be
Interval_finite_element
Method for representing and evaluating partial differential equations
contrasted with the finite difference methods, which approximate derivatives using nodal values, or finite element methods, which create local approximations
Finite_volume_method
Method for solving continuous operator problems (such as differential equations)
Galerkin methods are: the Galerkin method of weighted residuals, the most common method of calculating the global stiffness matrix in the finite element method
Galerkin_method
Type of differential equation
Meshfree methods include the generalized finite element method (GFEM), extended finite element method (XFEM), spectral finite element method (SFEM), meshfree
Partial_differential_equation
Numerical method
Finite Element-Discrete Element Method is contained in the book The Combined Finite-Discrete Element Method. The fundamental assumption of the method
Discrete_element_method
Technique to solve geological problems by computational simulation
Common methods include the finite element, finite difference, or finite volume method that subdivide the object of interest into smaller pieces (element) by
Numerical_modeling_(geology)
German engineer
mechanics. Bathe is considered to be one of the pioneers in the field of finite element analysis and its applications. He was born in Berlin as a second child
Klaus-Jürgen_Bathe
Analysis and solving of problems that involve fluid flows
Discrete element method Fictitious domain method Finite element method Finite volume method for unsteady flow Fluid animation Immersed boundary method Lattice
Computational_fluid_dynamics
Finite element model updating is the process of ensuring that finite element analysis results in models that better reflect the measured data than the
Finite_element_updating
Method for approximating eigenvalues
eigenfunction. In the context of the finite-element method, it is mathematically the same as the Ritz-Galerkin method. In mechanical and structural engineering
Rayleigh–Ritz_method
Branch of physics
modeled by finite element methods); matrix products (when using transfer matrix methods); calculating numerical integrals (when using the method of moments);
Computational electromagnetics
Computational_electromagnetics
Formulation of the finite element method
equations, a topic in mathematics, the spectral element method (SEM) is a formulation of the finite element method (FEM) that uses high-degree piecewise polynomials
Spectral_element_method
Methods in numerical analysis not requiring knowledge of neighboring points
the velocity field. Numerical methods such as the finite difference method, finite-volume method, and finite element method were originally defined on meshes
Meshfree_methods
Numerical method for solving certain differential equations
(1888–1937). It falls within the class of finite element methods. The hybrid Trefftz finite-element method has been considerably advanced since its introduction
Trefftz_method
Fibrous structure in the vestibular system of the inner ear
planets. The alternative method used for modeling the otolithic membrane is the finite difference method, while the finite element method has advantages in handling
Otolithic_membrane
Subfield of materials science
Many other methods exist, such as atomistic-continuum simulations, similar to QM/MM except using molecular dynamics and the finite element method as the fine
Computational materials science
Computational_materials_science
Numerical solution method of computational electromagnetics
The finite-difference frequency-domain (FDFD) method is a numerical solution method for problems usually in electromagnetism and sometimes in acoustics
Finite-difference frequency-domain method
Finite-difference_frequency-domain_method
the finite element method, it is useful to consider a set of functionals { f i } i = 1 n {\displaystyle \{f_{i}\}_{i=1}^{n}} that act on a finite dimensional
Unisolvent_functions
is followed. The finite difference scheme has an equivalent in the finite element method (Galerkin method). Another similar method is the characteristic
Numerical solution of the convection–diffusion equation
Numerical_solution_of_the_convection–diffusion_equation
The fuzzy finite element method combines the well-established finite element method with the concept of fuzzy numbers, the latter being a special case
Fuzzy_finite_element
Millennium Prize Problem
using techniques such as the finite element method or spectral methods. Here, we will use the finite difference method. To do this, we can divide the
Navier–Stokes existence and smoothness
Navier–Stokes_existence_and_smoothness
notable for our purposes are: finite difference methods, finite volume methods, finite element methods, and spectral methods. Finite difference replace the infinitesimal
Numerical methods in fluid mechanics
Numerical_methods_in_fluid_mechanics
consistent with the constraints See also: Interval boundary element method, Interval finite element Loss of significance Numerical error Numerical stability
List of numerical analysis topics
List_of_numerical_analysis_topics
Class of methods used in numerical analysis and scientific computing to solve ODE/PDE
Spectral methods and finite-element methods are closely related and built on the same ideas; the main difference between them is that spectral methods use
Spectral_method
Matrix used in finite element analysis
In the finite element method for the numerical solution of elliptic partial differential equations, the stiffness matrix is a matrix that represents the
Stiffness_matrix
Computational analysis of vibrations
object or structure during free vibration. It is common to use the finite element method (FEM) to perform this analysis because, like other calculations
Modal_analysis_using_FEM
Method of solving differential equations
Multigrid methods can be applied in combination with any of the common discretization techniques. For example, the finite element method may be recast
Multigrid_method
scientists and there are many articles on computer simulation, finite element method is one of the important approaches to understand the deformation
Equal channel angular extrusion
Equal_channel_angular_extrusion
Hungarian-born engineer (born 1935)
contributions on the finite element method, particularly the conception and implementation of the p- and hp-versions of the finite element method. He is a founding
Barna_Szabó
Calculation of structural loads
differential equation. The finite element method is perhaps the most restrictive and most useful at the same time. This method itself relies upon other
Structural_analysis
Methods for solving differential equations
methods (DG methods) form a class of numerical methods for solving differential equations. They combine features of the finite element and the finite
Discontinuous_Galerkin_method
engineering software which is used for computational fluid dynamics, finite element method structural analysis, flight dynamics, propulsion modeling, and other
List of aerospace engineering software
List_of_aerospace_engineering_software
Computational method for solving partial differential equations
complicated than the finite element method. Another advantage is it works well on multi variable problems. The finite element method is complicated when
Kansa_method
Project
concepts: the finite element method of structural analysis and the introduction of relatively low-cost microprocessors. In the finite element method, the behavior
Finite_element_machine
Simulation of multiple aspects of physics
implemented with discretization methods such as the finite element method, finite difference method, or finite volume method. Multiphysics simulations can
Multiphysics_simulation
German mathematician
equations. The duality argument for estimating the error of the finite element method and a scheme for the weak enforcement of Dirichlet boundary conditions
Joachim_Nitsche
Split of materials or structures under stress
numerical methods are finite element and boundary integral equation methods. Other methods include stress and displacement matching, element crack advance
Fracture
Method for numerical differential equations
in this case a nonconforming method for the approximation of (2), which includes the nonconforming finite element method. Note that the converse is not
Gradient discretisation method
Gradient_discretisation_method
Lemma in numerical analysis of differential equations
dissertation, it is an important tool for proving error estimates for the finite element method applied to elliptic partial differential equations. Let V {\displaystyle
Céa's_lemma
Numerical method in computational electromagnetics
conditions. This is done by using discrete meshes as in finite difference and finite element methods, often for the surface. The solutions are represented
Method of moments (electromagnetics)
Method_of_moments_(electromagnetics)
the governing equations are replaced by finite differences yielding an algebraic equation. Finite element method uses piece wise functions valid on elements
Application of CFD in thermal power plants
Application_of_CFD_in_thermal_power_plants
Finite element exterior calculus (FEEC) is a mathematical framework that formulates finite element methods using chain complexes. Its main application
Finite element exterior calculus
Finite_element_exterior_calculus
element method (NEM) is a meshless method to solve partial differential equation, where the elements do not have a predefined shape as in the finite element
Natural_element_method
American academic (born 1945)
Texas A&M University. He is known for his contributions to the finite element method, solid mechanics, plate theory, composite materials, and applied
J._N._Reddy_(engineer)
infinite element method is a numerical method for solving problems of engineering and mathematical physics. It is a modification of finite element method. The
Infinite_element_method
Czech-American mathematician (1926–2023)
finite element method and the proof of the Babuška–Lax–Milgram theorem in partial differential equations. One of the celebrated results in the finite
Ivo_Babuška
Construction Structural Analysis
versatile than the finite element method but is more efficient in terms of computation power in some situations. Cheung, Y.K. “Finite strip method in structural
Finite_strip_method
Virtual recreation of a destructive car crash
presented methods complement each other. Macro Element Method is useful at early stage of the structure design process while Finite Element Method performs
Crash_simulation
American mathematician
collaborated with John Osborn on the theory of the Ritz method in the finite element method context and with Nikolai Sergeevich Bakhvalov (Russian: Николай
Andrei Knyazev (mathematician)
Andrei_Knyazev_(mathematician)
Computer-aided design software
dynamic; electro-magnetic; thermal, using the finite element method; and fluid, using the finite volume method). Manufacturing finished design by using included
Siemens_NX
been mainly applied to design stabilized finite element methods in which stability of the standard Galerkin method is not ensured both in terms of singular
Variational_multiscale_method
Methods for numerical approximations
a finite-dimensional subspace. This can be done by a finite element method, a finite difference method, or (particularly in engineering) a finite volume
Numerical_analysis
The patch test in the finite element method is a simple indicator of the quality of a finite element, developed by Bruce Irons. The patch test uses a partial
Patch_test_(finite_elements)
British academic of Polish descent, mathematician and civil engineer
born in Caterham, England. He was one of the early pioneers of the finite element method. Since his first paper in 1947 dealing with numerical approximation
Olgierd_Zienkiewicz
and blanks prior to building try-out tooling. Finite element analysis (FEA) is the most common method of simulating sheet metal forming operations to
Sheet metal forming simulation
Sheet_metal_forming_simulation
Overview of casting simulation tools
numerical analysis methods are applied, among which the finite element method (FEM), finite difference method (FDM), and finite volume method (FVM) hold a special
Metal_casting_simulation
Branch of applied mechanics dealing with rotating structures
obtained from solving models numerically (Rayleigh–Ritz method) and finally from the finite element method (FEM), which is another approach for modelling and
Rotordynamics
approach to solving sparse linear systems which is used extensively in finite element analysis. Algorithms of this kind are variants of Gauss elimination
Frontal_solver
Numerical analysis technique
Finite-difference time-domain (FDTD) or Yee's method (named after the Chinese American applied mathematician Kane S. Yee, born 1934) is a numerical analysis
Finite-difference time-domain method
Finite-difference_time-domain_method
Generalization of finite element method
hp-FEM is a generalization of the finite element method (FEM) for solving partial differential equations numerically based on piecewise-polynomial approximations
Hp-FEM
American engineer
York: Springer, 1998. Thomas J. R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover Publications, 2000. Erwin Stein
Thomas_J.R._Hughes
in part of the dynamic analysis of structures discretized by the finite element method. In this case the quadratic, Q ( λ ) {\displaystyle Q(\lambda )}
Quadratic_eigenvalue_problem
Algorithm used for points in euclidean space
of Lloyd's algorithm include smoothing of triangle meshes in the finite element method. Example of Lloyd's algorithm. The Voronoi diagram of the current
Lloyd's_algorithm
Numerical simulation on electromagnets
Ansys HFSS (high-frequency structure simulator) is a commercial finite element method solver for electromagnetic (EM) structures from Ansys. Engineers
Ansys_HFSS
computational mechanics applications, particularly in finite element method and boundary element method, to mesh problem domains into elements. Coons patches
Coons_patch
Numerical technique to simulate behavior of continuous substances
other mesh-based methods like the finite element method, finite volume method or finite difference method, the MPM is not a mesh based method and is instead
Material_point_method
Open-source C++ library
C++ library for solving partial differential equations using the finite element method, developed and maintained by researchers at the Lawrence Livermore
MFEM
Type of numerical method
the finite element method, continuity of solutions between non-matching subdomains is implemented by multiple-point constraints. Finite element simulations
Domain_decomposition_methods
Differential calculus on function spaces
problems in Einstein's general theory of relativity; Finite element method is a variational method for finding numerical solutions to boundary-value problems
Calculus_of_variations
solution of sparse linear systems derived from two-dimensional finite element method meshes) the resulting matrix has O(n log n) nonzeros, due to the
Nested_dissection
Higher Studying Field
Flexibility method Direct stiffness method Finite element method in structural mechanics Plastic analysis Beam theory Buckling Earthquake engineering Finite element
Structural_mechanics
GE-SYSTEM, SciGlass, and Interglad, sometimes combined with the finite element method. For estimating melting enthalpy, thermodynamic databases are used
Calculation of glass properties
Calculation_of_glass_properties
Method for analyzing stability of slopes of soil or rock
layout optimization Discrete element method Finite difference method Finite element limit analysis Finite element method Mohr–Coulomb theory PLAXIS SMR
Slope_stability_analysis
Computer-aided tomographic process
CT Image-based finite element method converts the 3D image data from X-ray computed tomography directly into meshes for finite element analysis. Benefits
Industrial computed tomography
Industrial_computed_tomography
multifrontal method, which is a version of Gaussian elimination for large sparse systems of equations, especially those arising from the finite element method. It
MUMPS_(software)
Structure built to span physical obstacles
bridge engineers typically use limit state design processes and the finite element method. Many bridges are admired for their beauty, and some spectacular
Bridge
Mesoscale computational technique
one based on the finite element method known as Crystal Plasticity Finite Element Method (CPFEM), which is developed based on the finite strain formulation
Crystal_plasticity
Analog of the continuous Laplace operator
Approximations of the Laplacian, obtained by the finite-difference method or by the finite-element method, can also be called discrete Laplacians. For example
Discrete_Laplace_operator
The bilinear quadrilateral element, also known as the Q4 element, is a type of element used in finite element analysis which is used to approximate in
Bilinear quadrilateral element
Bilinear_quadrilateral_element
Division of the U.S. Naval Surface Warfare Center
Modeling and Simulation (M&S) techniques and coupled Boundary Element Method and Finite Element Method (BEM/FEM). Particular circuit M&S tools and BEM/FEM tools
Naval Surface Warfare Center Crane Division
Naval_Surface_Warfare_Center_Crane_Division
American engineer and academic (1920–2016)
of the finite element method (FEM). His 1956 article was one of the first applications of this computational method. He coined the term "finite elements"
Ray_William_Clough
Mathematical model for describing material deformation under stress
463 ISBN 0-471-98716-6 J. N. Reddy, David K. Gartling (2000) The finite element method in heat transfer and fluid dynamics, p. 317, CRC Press ISBN 1-4200-8598-0
Finite_strain_theory
Z88 is a software package for the finite element method (FEM) and topology optimization. A team led by Frank Rieg at the University of Bayreuth started
Z88_FEM_software
Finite element method for Navier-Stokes equations
equations can be used for finite element computations of high Reynolds number incompressible flow using equal order of finite element space (i.e. P k − P k
Streamline_upwind_Petrov–Galerkin_pressure-stabilizing_Petrov–Galerkin_formulation_for_incompressible_Navier–Stokes_equations
Mathematical method for optimizing material layout under given conditions
configurations. The conventional topology optimization formulation uses a finite element method (FEM) to evaluate the design performance. The design is optimized
Topology_optimization
French mathematician
known particularly for his work on mathematical analysis of the finite element method. He has contributed also to elasticity, to the theory of plates
Philippe_G._Ciarlet
Greek pioneer of computer applications
applications in science and engineering, among the creators of the finite element method (FEM), and later Professor at the University of Stuttgart and Director
John_Argyris
Structural analysis method
Wood–Armer method is a structural analysis method based on finite element analysis used to design the reinforcement for concrete slabs. This method provides
Wood–Armer_method
Free and open-source 3D CAD software
a building information modeling (BIM) software application with finite element method (FEM) support. It is intended for mechanical engineering product
FreeCAD
Vector basis functions
Raviart–Thomas basis functions are vector basis functions used in finite element and boundary element methods. They are regularly used as basis functions when working
Raviart–Thomas basis functions
Raviart–Thomas_basis_functions
FINITE ELEMENT-METHOD
FINITE ELEMENT-METHOD
Male
Italian
 Italian, Portuguese and Spanish form of Latin Clementius, CLEMENTE means "gentle and merciful."
Male
Russian
(Климент) Russian form of Greek Klementos, KLIMENT means "gentle and merciful."
Boy/Male
Australian, British, Danish, Dutch, English, Finnish, French, German, Irish, Latin, Swedish
Gentle; Merciful; Mild; Form of Clement
Male
English
Variant spelling of English Finnian, FINIAN means "little white one."
Girl/Female
Indian
Infinite, Divine
Male
English
Short form of Latin Clementius, CLEMENT means "gentle and merciful." meaning "gentle and merciful." In the bible, this is the name of a companion of Paul.
Male
Portuguese
Portuguese form of Latin Philippus, FILIPE means "lover of horses."
Male
Slovene
Slovene form of Greek Klementos, KLEMEN means "gentle and merciful."
Boy/Male
English
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Male
Polish
 Danish, German, Polish and Swedish form of Greek Klementos, KLEMENS means "gentle and merciful."
Boy/Male
African, American, Australian, British, Chinese, Christian, Danish, English, French, German, Greek, Indian, Jamaican, Latin, Swedish, Swiss
Merciful; Mild; Gentle; Giving Mercy; Merciful in French
Surname or Lastname
English, French, and Dutch
English, French, and Dutch : from the Latin personal name Clemens meaning ‘merciful’ (genitive Clementis). This achieved popularity firstly through having been borne by an early saint who was a disciple of St. Paul, and later because it was selected as a symbolic name by a number of early popes. There has also been some confusion with the personal name Clemence (Latin Clementia, meaning ‘mercy’, an abstract noun derived from the adjective; in part a masculine name from Latin Clementius, a later derivative of Clemens). As an American family name, Clement has absorbed cognates in other continental European languages. (For forms, see Hanks and Hodges 1988.)
Surname or Lastname
English
English : patronymic from the personal name Clement. As an American family name, this form has absorbed cognates in other continental European languages. (For forms, see Hanks and Hodges 1988.)
Boy/Male
English American Biblical Latin
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Boy/Male
English
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Boy/Male
Czechoslovakian, Danish, German, Greek, Latin, Polish
Giving Mercy; Mild; Merciful
Male
English
English surname transferred to forename use, derived from Latin Clemens or Clement, CLEMENTS means "gentle and merciful."
Surname or Lastname
English
English : patronymic from the personal name Clement.German, Dutch, and Danish : from the personal name Clemens (see Clement).Samuel Langhorne Clemens, better known by his pen name, Mark Twain, was descended from VA stock on his father’s side, from a Robert Clemens, who was born in Warwickshire, England, in 1634.
Male
Hungarian
Hungarian form of Greek Klementos, KELEMEN means "gentle and merciful."
Boy/Male
English American Danish
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
FINITE ELEMENT-METHOD
FINITE ELEMENT-METHOD
Biblical
vine; hissing; a color inclining to yellow
Boy/Male
Hindu
Name of a Hindu month, Name of a star
Boy/Male
Arabic, Muslim
Kind of Spear
Girl/Female
Tamil
Tinkling, Cute and pretty
Boy/Male
Hindu
Calm, Unmovable, Unshakable
Girl/Female
Indian
Cool and fresh breeze of morning
Girl/Female
Tamil
Humility
Male
Hebrew
(יָקְטָן) Hebrew name YOQTAN means "small." In the bible, this is the name of a descendant of Shem. Joktan is the Anglicized form.
Girl/Female
Muslim
Beauty
Girl/Female
Tamil
Worshipped
FINITE ELEMENT-METHOD
FINITE ELEMENT-METHOD
FINITE ELEMENT-METHOD
FINITE ELEMENT-METHOD
FINITE ELEMENT-METHOD
n.
One out of several parts combined in a system of aggregation, when each is of the nature of the whole; as, a single cell is an element of the honeycomb.
v. t.
To constitute; to make up with elements.
n.
Sometimes a curve, or surface, or volume is considered as described by a moving point, or curve, or surface, the latter being at any instant called an element of the former.
a.
Pertaining to the elements, first principles, and primary ingredients, or to the four supposed elements of the material world; as, elemental air.
a.
Constituting one of eleven parts into which a thing is divided; as, the eleventh part of a thing.
n.
Any outline or sketch, regarded as containing the fundamental ideas or features of the thing in question; as, the elements of a plan.
a.
Without limit in power, capacity, knowledge, or excellence; boundless; immeasurably or inconceivably great; perfect; as, the infinite wisdom and goodness of God; -- opposed to finite.
v. t.
To compound of elements or first principles.
n.
See Yenite.
n.
The four elements were, air, earth, water, and fire
n.
One of the necessary data or values upon which a system of calculations depends, or general conclusions are based; as, the elements of a planet's orbit.
n.
To unite or cause to adhere by means of a cement.
n.
An infinitesimal part of anything of the same nature as the entire magnitude considered; as, in a solid an element may be the infinitesimal portion between any two planes that are separated an indefinitely small distance. In the calculus, element is sometimes used as synonymous with differential.
n.
The elements of the alchemists were salt, sulphur, and mercury.
n.
See Conite.
n.
The simplest or fundamental principles of any system in philosophy, science, or art; rudiments; as, the elements of geometry, or of music.
a.
Acting with great force; furious; violent; impetuous; forcible; mighty; as, vehement wind; a vehement torrent; a vehement fire or heat.
n.
One of the ultimate parts which are variously combined in anything; as, letters are the elements of written language; hence, also, a simple portion of that which is complex, as a shaft, lever, wheel, or any simple part in a machine; one of the essential ingredients of any mixture; a constituent part; as, quartz, feldspar, and mica are the elements of granite.
a.
Having a limit; limited in quantity, degree, or capacity; bounded; -- opposed to infinite; as, finite number; finite existence; a finite being; a finite mind; finite duration.
adv.
In a finite manner or degree.