The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical...

common approaches to the numerical solution of PDE, along with finite element methods. For a n-times differentiable function, by Taylor's theorem the...

extended finite element method (XFEM), is a numerical technique based on the generalized finite element method (GFEM) and the partition of unity method (PUM)...

The finite element method (FEM) is a powerful technique originally developed for numerical solution of complex problems in structural mechanics, and it...

In numerical analysis, the mixed finite element method, is a type of finite element method in which extra fields to be solved are introduced during the...

contrasted with the finite difference methods, which approximate derivatives using nodal values, or finite element methods, which create local approximations...

Smoothed finite element methods (S-FEM) are a particular class of numerical simulation algorithms for the simulation of physical phenomena. It was developed...

Galerkin methods are: the Galerkin method of weighted residuals, the most common method of calculating the global stiffness matrix in the finite element method...

nonconforming finite element, mixed finite element, mimetic finite difference...) inherit these convergence properties. The finite-volume method is a numerical...

This is a list of notable software packages that implement the finite element method for solving partial differential equations. This table is contributed...

boundary element methods are significantly less efficient than volume-discretisation methods (finite element method, finite difference method, finite volume...

Finite Element-Discrete Element Method is contained in the book The Combined Finite-Discrete Element Method. The fundamental assumption of the 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...

Meshfree methods include the generalized finite element method (GFEM), extended finite element method (XFEM), spectral finite element method (SFEM), meshfree...

Discrete element method Finite element method Finite volume method for unsteady flow Fluid animation Immersed boundary method Lattice Boltzmann methods List...

infinite element method is a numerical method for solving problems of engineering and mathematical physics. It is a modification of finite element method. The...

modeled by finite element methods); matrix products (when using transfer matrix methods); calculating numerical integrals (when using the method of moments);...

consistent with the constraints See also: Interval boundary element method, Interval finite element Loss of significance Numerical error Numerical stability...

the Ritz method uses trial wave functions to approximate the ground state eigenfunction with the lowest energy. In the finite element method context,...

differential equation. The finite element method is perhaps the most restrictive and most useful at the same time. This method itself relies upon other...

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,...

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...

supraconvergent method is one which converges faster than generally expected (superconvergence or supraconvergence). For example, in the Finite Element Method approximation...

Common methods include the finite element, finite difference, or finite volume method that subdivide the object of interest into smaller pieces (element) by...

The finite-difference frequency-domain (FDFD) method is a numerical solution method for problems usually in electromagnetism and sometimes in acoustics...

Euler's forward method Explicit and implicit methods (numerical analysis) Finite difference method (numerical analysis) Finite element method (numerical analysis)...

methods (DG methods) form a class of numerical methods for solving differential equations. They combine features of the finite element and the finite...

a finite-dimensional subspace. This can be done by a finite element method, a finite difference method, or (particularly in engineering) a finite volume...

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...

notable for our purposes are: finite difference methods, finite volume methods, finite element methods, and spectral methods. Finite difference replace the infinitesimal...