We devise a Hybrid High-Order (HHO) method for highly oscillatory elliptic problems that is capable of handling general meshes. The method hinges on discrete unknowns that are polynomials attached to the faces and cells of a coarse mesh; those attached to the cells can be eliminated locally using static condensation. The main building ingredient is a reconstruction operator, local to each coarse cell, that maps onto a fine-scale space spanned by oscillatory basis functions. The present HHO method generalizes the ideas of some existing multiscale approaches, while providing the first complete analysis on general meshes. It also improves on those methods, taking advantage of the flexibility granted by the HHO framework. The method handles arbitrary orders of approximation k ≥ 0. For face unknowns that are polynomials of degree k, we devise two versions of the method, depending on the polynomial degree (k − 1) or k of the cell unknowns. We prove, in the case of periodic coefficients, an energy-error estimate of the form (ε 1 2 + Hk+1 + (Hε ) 2 1 ), and we illustrate our theoretical findings on some test-cases.
A hybrid high-order method for highly oscillatory elliptic problems / Cicuttin, M.; Ern, A.; Lemaire, S.. - In: COMPUTATIONAL METHODS IN APPLIED MATHEMATICS. - ISSN 1609-4840. - ELETTRONICO. - 19:4(2019), pp. 723-748. [10.1515/cmam-2018-0013]
A hybrid high-order method for highly oscillatory elliptic problems
Cicuttin M.;
2019
Abstract
We devise a Hybrid High-Order (HHO) method for highly oscillatory elliptic problems that is capable of handling general meshes. The method hinges on discrete unknowns that are polynomials attached to the faces and cells of a coarse mesh; those attached to the cells can be eliminated locally using static condensation. The main building ingredient is a reconstruction operator, local to each coarse cell, that maps onto a fine-scale space spanned by oscillatory basis functions. The present HHO method generalizes the ideas of some existing multiscale approaches, while providing the first complete analysis on general meshes. It also improves on those methods, taking advantage of the flexibility granted by the HHO framework. The method handles arbitrary orders of approximation k ≥ 0. For face unknowns that are polynomials of degree k, we devise two versions of the method, depending on the polynomial degree (k − 1) or k of the cell unknowns. We prove, in the case of periodic coefficients, an energy-error estimate of the form (ε 1 2 + Hk+1 + (Hε ) 2 1 ), and we illustrate our theoretical findings on some test-cases.File | Dimensione | Formato | |
---|---|---|---|
10.1515_cmam-2018-0013.pdf
accesso aperto
Tipologia:
2a Post-print versione editoriale / Version of Record
Licenza:
Pubblico - Tutti i diritti riservati
Dimensione
883.14 kB
Formato
Adobe PDF
|
883.14 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11583/2978973