Name
Title | ||
|---|---|---|
Stability and Convergence of a Class of Finite Element Schemes for Hyperbolic Systems of Conservation Laws |
Abstract | ||
|---|---|---|
We propose a class of finite element schemes for systems of hyperbolic conservation laws that are based on finite element discretizations of appropriate relaxation models. We consider both semidiscrete and fully discrete finite element schemes and show that the schemes are stable and, when the compensated compactness theory is applicable, do converge to a weak solution of the hyperbolic system. The schemes use piecewise polynomials of arbitrary degree and their consistency error is of high order. We also prove that the rate of convergence of the relaxation system to a smooth solution of the conservation laws is of order $O(\eps )$. |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1137/S0036142902420436 | SIAM J. Numerical Analysis |
Keywords | Field | DocType |
discrete finite element scheme,finite element discretizations,. stability and convergence,finite element scheme,smooth solution,hyperbolic systems,conservation law,finite element schemes,hyperbolic system,relaxation system,high order,conservation laws,hyperbolic conservation law,hyperbolic conservation laws. 1,appropriate relaxation model,finite element,weak solution | Stability criterion,Mathematical optimization,Mathematical analysis,Weak solution,Finite element method,Rate of convergence,Numerical stability,Mathematics,Conservation law,Piecewise,Mixed finite element method | Journal |
Volume | Issue | ISSN |
42 | 4 | 0036-1429 |
Citations | PageRank | References |
9 | 1.34 | 4 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Christos Arvanitis | 1 | 12 | 2.18 |
| Charalambos Makridakis | 2 | 253 | 48.36 |
| Athanasios E. Tzavaras | 3 | 27 | 11.12 |