Publication

Tunable Integration Scheme for the Finite-Element Method

1991
Journal Articles

Abstract

A discretization method is proposed where a tunable integration scheme is applied to the finite element method (FEM). The method is characterized by one continuous parameter, p. A theoretical error analysis is given and three different eigenvalue problems are used as test cases: a simple example with constant coefficients and two model problems from ideal and resistive magnetohydrodynamics. It is shown that, for judicious choices of p, the tunable integration method clearly improves the convergence of the strict FEM. The sensitivity to the choice of integration parameter is discussed.

Official source

https://infoscience.epfl.ch/entities/publication/da88c253-2654-4553-b3a2-301285e69e38

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1991
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/da88c253-2654-4553-b3a2-301285e69e38

About this result

Related concepts (32)

Finite difference method

In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points.

Finite element method

The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).

Euler method

In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).

Related publications (32)

Tunable Integration Scheme for the Finite-Element Method

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