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.

Hybrid High-Order Methods for the Elliptic Obstacle Problem / Cicuttin, M.; Ern, A.; Gudi, T.. - In: JOURNAL OF SCIENTIFIC COMPUTING. - ISSN 0885-7474. - ELETTRONICO. - 83:1(2020). [10.1007/s10915-020-01195-z]

### Hybrid High-Order Methods for the Elliptic Obstacle Problem

#### 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.
##### Scheda breve Scheda completa Scheda completa (DC) 2020
File in questo prodotto:
File
Hybrid High-Order Methods for the Elliptic Obstacle Problem.pdf

non disponibili

Tipologia: 2a Post-print versione editoriale / Version of Record
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 617.52 kB
Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11583/2978977`