Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the convergence of a finite element method for a nonlinear hyperbolic conservation law
HTML articles powered by AMS MathViewer

by Claes Johnson and Anders Szepessy PDF
Math. Comp. 49 (1987), 427-444 Request permission

Abstract:

We consider a space-time finite element discretization of a time-dependent nonlinear hyperbolic conservation law in one space dimension (Burgers’ equation). The finite element method is higher-order accurate and is a Petrov-Galerkin method based on the so-called streamline diffusion modification of the test functions giving added stability. We first prove that if a sequence of finite element solutions converges boundedly almost everywhere (as the mesh size tends to zero) to a function u, then u is an entropy solution of the conservation law. This result may be extended to systems of conservation laws with convex entropy in several dimensions. We then prove, using a compensated compactness result of Murat-Tartar, that if the finite element solutions are uniformly bounded then a subsequence will converge to an entropy solution of Burgers’ equation. We also consider a further modification of the test functions giving a method with improved shock capturing. Finally, we present the results of some numerical experiments.
References
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 65M10, 65M60
  • Retrieve articles in all journals with MSC: 65M10, 65M60
Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Math. Comp. 49 (1987), 427-444
  • MSC: Primary 65M10; Secondary 65M60
  • DOI: https://doi.org/10.1090/S0025-5718-1987-0906180-5
  • MathSciNet review: 906180