Evolution Galerkin methods for hyperbolic systems in two space dimensions. (English) Zbl 0951.35076
Three new evolution Galerkin schemes for multidimensional hyperbolic systems are presented. The wave equations system is considered in more details. An algorithm for constructing of an evolution Galerkin scheme consists of two steps: first an integral representation of the exact evolution operator is obtained; then the solution is projected in a finite element space. A theoretical analysis of stability properties of the scheme is given and error estimates are obtained. New evolution Galerkin schemes are compared with several existing schemes by means of calculations of test problems in two space dimensions on rectangular grids.
Reviewer: Ramaz Bochorishvili (Tbilisi)
MSC:
| 35L45 | Initial value problems for first-order hyperbolic systems |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35L65 | Hyperbolic conservation laws |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
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