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Journal of Scientific Computing

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01-04-2020

Hybrid High-Order Methods for the Elliptic Obstacle Problem

Authors: Matteo Cicuttin, Alexandre Ern, Thirupathi Gudi

Published in: Journal of Scientific Computing | Issue 1/2020

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Abstract

Hybrid High-Order methods are introduced and analyzed for the elliptic obstacle problem in two and three space dimensions. The methods are formulated in terms of face unknowns which are polynomials of degree \(k=0\) or \(k=1\) and in terms of cell unknowns which are polynomials of degree \(l=0\). The discrete obstacle constraints are enforced on the cell unknowns. Higher polynomial degrees are not considered owing to the modest regularity of the exact solution. A priori error estimates of optimal order, that is, up to the expected regularity of the exact solution, are shown. Specifically, for \(k=1\), the method employs a local quadratic reconstruction operator and achieves an energy-error estimate of order \(h^{\frac{3}{2}-\epsilon }\), \(\epsilon >0\). To our knowledge, this result fills a gap in the literature for the quadratic approximation of the three-dimensional obstacle problem. Numerical experiments in two and three space dimensions illustrate the theoretical results.

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Title: Hybrid High-Order Methods for the Elliptic Obstacle Problem
Authors: Matteo Cicuttin
Alexandre Ern
Thirupathi Gudi
Publication date: 01-04-2020
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2020
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-020-01195-z

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