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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
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