Exponential convergence of the hp virtual element method in presence of corner singularities

Exponential convergence of the hp virtual element method in presence of corner singularities In the present work, we analyze the hp version of virtual element methods for the 2D Poisson problem. We prove exponential convergence of the energy error employing sequences of polygonal meshes geometrically refined, thus extending the classical choices for the decomposition in the hp finite element framework to very general decomposition of the domain. A new stabilization for the discrete bilinear form with explicit bounds in h and $$p$$ p is introduced. Numerical experiments validate the theoretical results. We also exhibit a numerical comparison between hp virtual elements and hp finite elements. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Numerische Mathematik Springer Journals

Exponential convergence of the hp virtual element method in presence of corner singularities

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by The Author(s)
Subject
Mathematics; Numerical Analysis; Mathematics, general; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation; Mathematical and Computational Engineering
ISSN
0029-599X
eISSN
0945-3245
D.O.I.
10.1007/s00211-017-0921-7
Publisher site
See Article on Publisher Site

Abstract

In the present work, we analyze the hp version of virtual element methods for the 2D Poisson problem. We prove exponential convergence of the energy error employing sequences of polygonal meshes geometrically refined, thus extending the classical choices for the decomposition in the hp finite element framework to very general decomposition of the domain. A new stabilization for the discrete bilinear form with explicit bounds in h and $$p$$ p is introduced. Numerical experiments validate the theoretical results. We also exhibit a numerical comparison between hp virtual elements and hp finite elements.

Journal

Numerische MathematikSpringer Journals

Published: Oct 25, 2017

References

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