ANALYSIS OF A CONTINUOUS FINITE ELEMENT METHOD FOR HYPERBOLIC EQUATIONS.

Richard S. Falk, Gerard R. Richter

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

A finite element method for hyperbolic equations is analyzed in the context of a first order linear problem in R**2. The method is applicable over a triangulation of the domain, and produces a continuous piecewise polynomial approximation, which can be developed in an explicit fashion from triangle to triangle. In a sense, it extends the basic upwind difference scheme to higher order. The method is shown to be stable, and error estimates are obtained. For nth degree approximation, the errors in the approximate solution and its gradient are shown to be at least of order h**n** plus ** one quarter and h**n** minus ** one-half , respectively, assuming sufficient regularity in the solution.

Original languageEnglish (US)
Pages (from-to)257-278
Number of pages22
JournalSIAM Journal on Numerical Analysis
Volume24
Issue number2
DOIs
StatePublished - Jan 1 1987

Fingerprint

Hyperbolic Equations
Triangle
Finite Element Method
Finite element method
Polynomial approximation
Upwind Scheme
Piecewise Polynomials
Polynomial Approximation
Triangulation
Difference Scheme
Error Estimates
Approximate Solution
Regularity
Higher Order
Sufficient
Gradient
First-order
Approximation
Context

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

Falk, Richard S. ; Richter, Gerard R. / ANALYSIS OF A CONTINUOUS FINITE ELEMENT METHOD FOR HYPERBOLIC EQUATIONS. In: SIAM Journal on Numerical Analysis. 1987 ; Vol. 24, No. 2. pp. 257-278.
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ANALYSIS OF A CONTINUOUS FINITE ELEMENT METHOD FOR HYPERBOLIC EQUATIONS. / Falk, Richard S.; Richter, Gerard R.

In: SIAM Journal on Numerical Analysis, Vol. 24, No. 2, 01.01.1987, p. 257-278.

Research output: Contribution to journalArticle

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