Stable broken H1 and Hdiv polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensionsReport as inadecuate




Stable broken H1 and Hdiv polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions - Download this document for free, or read online. Document in PDF available to download.

* Corresponding author 1 CERMICS - Centre d-Enseignement et de Recherche en Mathématiques et Calcul Scientifique 2 SERENA - Simulation for the Environment : Reliable and Efficient Numerical Algorithms Inria Paris-Rocquencourt

Abstract : We study extensions of piecewise polynomial data prescribed on faces and possibly in elements of a patch of simplices sharing a vertex. In the H1 setting, we look for functions whose jumps across the faces are prescribed, whereas in the Hdiv setting, the normal component jumps and the piecewise divergence are prescribed. We show stability in the sense that the minimizers over piecewise polynomial spaces of the same degree as the data are subordinate in the broken energy norm to the minimizers over the whole broken H1 and Hdiv spaces. Our proofs are constructive and yield constants independent of the polynomial degree. One particular application of these results is in a posteriori error analysis, where the present results justify polynomial-degree-robust efficiency of potential and flux reconstructions.

Keywords : polynomial extension operator broken Sobolev space potential reconstruction flux reconstruction a posteriori error estimate robustness polynomial degree best approximation patch of elements





Author: Alexandre Ern - Martin Vohralík -

Source: https://hal.archives-ouvertes.fr/



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