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Piecewise \(\mathrm{H}^1\) functions and vector fields associated with meshes generated by independent refinements. (English) Zbl 1311.65143

Summary: We consider piecewise \( H^1\) functions and vector fields associated with a class of meshes generated by independent refinements and show that they can be effectively analyzed in terms of the number of refinement levels and the shape regularity of the subdomains that appear in the meshes. We derive Poincaré-Friedrichs inequalities and Korn’s inequalities for such meshes and discuss an application to a discontinuous finite element method.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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