Discontinuous Galerkin approximation of the Laplace eigenproblem. (English) Zbl 1168.65410
Summary: We analyse the problem of computing eigenvalues and eigenfunctions of the Laplace operator by means of discontinuous Galerkin (DG) methods. It results that several DG methods actually provide a spectrally correct approximation of the Laplace operator. We present here the convergence theory, which applies to a wide class of DG methods, as well as numerical tests demonstrating the theoretical results.
MSC:
| 65N25 | Numerical methods for eigenvalue problems for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35P15 | Estimates of eigenvalues in context of PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
Keywords:
discontinuous Galerkin methods; eigenvalue problems; numerical examples; eigenfunctions; Laplace operator; convergenceReferences:
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