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Recovery-based error estimators for the VEM and BEM-based FEM. (English) Zbl 1454.65172

The authors are concerned with the development and analysis of gradient recovery techniques for the first order BEM-based FEM, a technique that incorporates BEM techniques into the FEM framework, and VEM, i.e., a generalization of the FEM designed to extend the method to arbitrary polygonal or polyhedral elements. First, they show the existence of superconvergent points for the BEM-based FEM and proceed with constructing superconvergent gradients. They observe that BEM-based FEM as well as the VEM are not restricted to first order. Then the superconvergence is used in the reconstruction of the gradient of the finite element solution in order to obtain a more accurate approximation of the true gradient. In the last two sections the gradient recovery technique is used in order to formulate a posteriori error estimators for both methods.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N38 Boundary element methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs

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