Convergence of finite element method for linear second-order wave equations with discontinuous coefficients. (English) Zbl 1274.65255
Summary: A finite element method is proposed and analyzed for hyperbolic problems with discontinuous coefficients. The main emphasize is given on the convergence of such method. Due to low global regularity of the solutions, the error analysis of the standard finite element method is difficult to adopt for such problems. For a practical finite element discretization, optimal error estimates in \(L^{\infty }(L^{2})\) and \(L^{\infty }(H^{1})\) norms are established for continuous time discretization. Further, a fully discrete scheme based on a symmetric difference approximation is considered, and optimal order convergence in \(L^{\infty }(H^{1})\) norm is established.
MSC:
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
finite element method; fully discrete scheme; hyperbolic; interface; optimal error estimates; semidiscrete schemeReferences:
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