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Spectral inclusion and spectral exactness for PDEs on exterior domains. (English) Zbl 1057.65079

Using the Dirichlet to Neumann map on the inner boundary, the authors give a method to identify spurious computed eigenvalues of elliptic partial differential equations (PDEs) on exterior domains. The method relies on the concepts of spectral inclusion and spectral exactness. To obtain results for non-self-adjoint problem the authors make certain additional assumptions. Their verification is discussed on presented examples. Numerical examples illustrate the efficiency of the method.

MSC:

65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
35P15 Estimates of eigenvalues in context of PDEs
35J25 Boundary value problems for second-order elliptic equations
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