Hybrid high-order methods for variable-diffusion problems on general meshes

By Daniele A. Di Pietro, Alexandre Ern. 2015

127 citations recorded by the source corpus.

We extend the Hybrid High-Order method introduced by the authors for the Poisson problem to problems with heterogeneous/anisotropic diffusion. The cornerstone is a local discrete gradient reconstruction from element- and face-based polynomial degrees of freedom. Optimal error estimates are proved.

Subfields: Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/60f9a2011e5af21963c486c4c9aa3d416e930a97

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

SUPG stabilization for the nonconforming virtual element method for advection–diffusion–reaction equations (2018, methodology): “Other methods or families of methods that are available from the literature include the polygonal/polyhedral finite element method (PFEM) [32, 33], the BEM-based FEM [34, 35], the finite volume methods [36, 37], hybrid high-order (HHO) method [38], the discontinuous Galerkin (DG) method [39, 40], an”
Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods (2016, methodology): “We consider here its application (studied in [17, 18]) to the numerical approximation of the model problem: find u P H(1) 0 pΩq such that ż”
Virtual Element Methods for general second order elliptic problems on polygonal meshes (2014, unknown): “See [22], [30], [31], [32], , [33], [35], [36], [37], [39], [55], [54], [56], [68], [69].”