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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