A fictitious domain method and its error estimate for second order hyperbolic problems. (Chinese. English summary) Zbl 1212.65402
Summary: Based on the essence of Lagrange multipliers, a fictitious domain method, especially for second order hyperbolic problems, is proposed, where all computational tasks are carried out in an auxiliary simply shaped domain in which the original domain is embedded. The simplicity of the auxiliary domain enables us to use uniform meshes to construct the finite element space and deduce a distinguished stiffness matrix. Finally, stability, convergence and error estimates are obtained for discrete schemes.
MSC:
65M85 | Fictitious domain 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 |
65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |