Higher order triangular finite elements with mass lumping for the wave equation

G. Cohen; P. Joly; J. E. Roberts; N. Tordjman

doi:10.1137/S0036142997329554

Higher order triangular finite elements with mass lumping for the wave equation

G. Cohen, P. Joly, J. E. Roberts, N. Tordjman

INRIA Institut National de Recherche en Informatique et en Automatique

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, we construct new higher order finite element spaces for the approximation of the two-dimensional (2D) wave equation. These elements lead to explicit methods after time discretization through the use of appropriate quadrature formulas which permit mass lumping. These formulas are constructed explicitly. Error estimates are provided for the corresponding semidiscrete problem. Finally, higher order finite difference time discretizations are proposed and various numerical results are shown.

Original language	English
Pages (from-to)	2047-2078
Number of pages	32
Journal	SIAM Journal on Numerical Analysis
Volume	38
Issue number	6
DOIs	https://doi.org/10.1137/S0036142997329554
Publication status	Published - 1 Dec 2001

Keywords

Finite elements
Mass lumping
Wave equation

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10.1137/S0036142997329554

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title = "Higher order triangular finite elements with mass lumping for the wave equation",

abstract = "In this article, we construct new higher order finite element spaces for the approximation of the two-dimensional (2D) wave equation. These elements lead to explicit methods after time discretization through the use of appropriate quadrature formulas which permit mass lumping. These formulas are constructed explicitly. Error estimates are provided for the corresponding semidiscrete problem. Finally, higher order finite difference time discretizations are proposed and various numerical results are shown.",

keywords = "Finite elements, Mass lumping, Wave equation",

author = "G. Cohen and P. Joly and Roberts, \{J. E.\} and N. Tordjman",

year = "2001",

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AU - Joly, P.

AU - Roberts, J. E.

AU - Tordjman, N.

PY - 2001/12/1

Y1 - 2001/12/1

N2 - In this article, we construct new higher order finite element spaces for the approximation of the two-dimensional (2D) wave equation. These elements lead to explicit methods after time discretization through the use of appropriate quadrature formulas which permit mass lumping. These formulas are constructed explicitly. Error estimates are provided for the corresponding semidiscrete problem. Finally, higher order finite difference time discretizations are proposed and various numerical results are shown.

AB - In this article, we construct new higher order finite element spaces for the approximation of the two-dimensional (2D) wave equation. These elements lead to explicit methods after time discretization through the use of appropriate quadrature formulas which permit mass lumping. These formulas are constructed explicitly. Error estimates are provided for the corresponding semidiscrete problem. Finally, higher order finite difference time discretizations are proposed and various numerical results are shown.

KW - Finite elements

KW - Mass lumping

KW - Wave equation

U2 - 10.1137/S0036142997329554

DO - 10.1137/S0036142997329554

M3 - Article

AN - SCOPUS:0041909738

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EP - 2078

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 6

ER -

Higher order triangular finite elements with mass lumping for the wave equation

Abstract

Keywords

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