Numerical solution of a two-dimensional hyperbolic transmission problem. (English) Zbl 1208.65129
An initial boundary value problem for a two-dimensional hyperbolic equation on a domain consisting of two disjoint rectangles is considered. The existence and uniqueness as well as a priori estimates for a weak solution in appropriate Sobolev-like spaces are proved. Various finite difference schemes are proposed and analyzed.
Reviewer: Iwan Gawriljuk (Eisenach)
MSC:
| 65M06 | Finite difference 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 |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35L20 | Initial-boundary value problems for second-order hyperbolic equations |
Keywords:
hyperbolic transmission problem; disjoint domains; finite difference scheme; convergence rate; error estimates; initial-boundary value problem; Sobolev spaces; weak solutionReferences:
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