We propose and validate a novel extension of Hybrid High-Order (HHO) methods to meshes featuring curved elements. HHO methods are based on discrete unknowns that are broken polynomials on the mesh and its skeleton. We propose here the use of physical frame polynomials over mesh elements and reference frame polynomials over mesh faces. With this choice, the degree of face unknowns must be suitably selected in order to recover on curved meshes the same convergence rates as on straight meshes. We provide an estimate of the optimal face polynomial degree depending on the element polynomial degree and on the so-called effective mapping order. The estimate is numerically validated through specifically crafted numerical tests. All test cases are conducted considering two- and three-dimensional pure diffusion problems, and include comparisons with discontinuous Galerkin discretizations. The extension to agglomerated meshes with curved boundaries is also considered.

(2018). Assessment of Hybrid High-Order methods on curved meshes and comparison with discontinuous Galerkin methods [journal article - articolo]. In JOURNAL OF COMPUTATIONAL PHYSICS. Retrieved from http://hdl.handle.net/10446/125389

Assessment of Hybrid High-Order methods on curved meshes and comparison with discontinuous Galerkin methods

Botti, Lorenzo;
2018-01-01

Abstract

We propose and validate a novel extension of Hybrid High-Order (HHO) methods to meshes featuring curved elements. HHO methods are based on discrete unknowns that are broken polynomials on the mesh and its skeleton. We propose here the use of physical frame polynomials over mesh elements and reference frame polynomials over mesh faces. With this choice, the degree of face unknowns must be suitably selected in order to recover on curved meshes the same convergence rates as on straight meshes. We provide an estimate of the optimal face polynomial degree depending on the element polynomial degree and on the so-called effective mapping order. The estimate is numerically validated through specifically crafted numerical tests. All test cases are conducted considering two- and three-dimensional pure diffusion problems, and include comparisons with discontinuous Galerkin discretizations. The extension to agglomerated meshes with curved boundaries is also considered.
articolo
2018
Botti, Lorenzo Alessio; Di Pietro, Daniele A.
(2018). Assessment of Hybrid High-Order methods on curved meshes and comparison with discontinuous Galerkin methods [journal article - articolo]. In JOURNAL OF COMPUTATIONAL PHYSICS. Retrieved from http://hdl.handle.net/10446/125389
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/125389
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