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A domain embedding method for Dirichlet problems in arbitrary space dimension. (English) Zbl 0913.65099
Author’s abstract: An embedding method for the discretization of Dirichlet boundary value problems over general domains in arbitrary space dimension is proposed. The main advantage of the method lies in the use of Cartesian coordinates independent of the underlying domain. Error estimates and aspects of the numerical realization are considered. To obtain an efficient solver for the resulting linear system of equations an easy-to-use preconditioning is recommended and analyzed. A variety of numerical experiments illustrate and confirm the theoretical results.
Reviewer: Th.Sonar (Hamburg)

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N15 Error bounds for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
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