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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:370

Article

Botti, Lorenzo¹  Di Pietro, Daniele A.² 

[1] Univ Bergamo, Dept Engn & Appl Sci, Bergamo, Italy

[2] Univ Montpellier, CNRS, Inst Montpellierain Alexander Grothendieck, Montpellier, France

关键词: Hybrid High-Order methods;    Discontinuous Galerkin methods;    Curved meshes;    Curved elements;    Poisson problem;   

DOI  :  10.1016/j.jcp.2018.05.017

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free