Hybrid High-Order Methods for the Elliptic Obstacle Problem

Cicuttin, M and Ern, A and Gudi, T (2020) Hybrid High-Order Methods for the Elliptic Obstacle Problem. In: Journal of Scientific Computing, 83 (1).

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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 h32-ϵ, ϵ> 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.

Item Type:	Journal Article
Publication:	Journal of Scientific Computing
Publisher:	Springer
Additional Information:	The copyright of this article belongs to Springer
Keywords:	Errors; Variational techniques, Discontinuous-skeletal method; Error estimates; High-order methods; Obstacle problems; Variational inequalities, Polynomials
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	19 Jun 2020 07:30
Last Modified:	19 Jun 2020 07:30
URI:	http://eprints.iisc.ac.in/id/eprint/65050

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