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A discontinuous Galerkin reduced basis element method for elliptic problems. (English) Zbl 1343.65132

This paper deals with a discontinuous Galerkin reduced basis element (DGRBE) which represents in fact a generalization and an improvement of both the reduced basis-domain decomposition-finite element method and the reduced basis hybrid method. The DGRBE approximation is based upon a set of local basis functions that feature nonhomogeneous Neumann boundary conditions.
The authors prove the well-posedness of the method, its stability and some convergence estimates. Some numerical tests are presented.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs

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