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A hybrid high‐order formulation for a Neumann problem on polytopal meshes
Author(s) -
Bustinza Rommel,
MunguiaLaCotera Jonathan
Publication year - 2020
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22439
Subject(s) - mathematics , polygon mesh , neumann boundary condition , stencil , operator (biology) , finite element method , degrees of freedom (physics and chemistry) , element (criminal law) , laplace operator , boundary (topology) , matching (statistics) , elliptic operator , order (exchange) , polynomial , mathematical analysis , geometry , computational science , biochemistry , chemistry , physics , repressor , quantum mechanics , finance , political science , transcription factor , law , economics , gene , thermodynamics , statistics
In this work, we study a hybrid high‐order (HHO) method for an elliptic diffusion problem with Neumann boundary condition. The proposed method has several features, such as: (a) the support of arbitrary approximation order polynomial at mesh elements and faces on polytopal meshes, (b) the design of a local (element‐wise) potential reconstruction operator and a local stabilization term, that weakly enforces the matching between local element‐ and face‐based on degrees of freedom, and (c) cheap computational cost, thanks to static condensation and compact stencil. We prove the well‐posedness of our HHO formulation, and obtain the optimal error estimates, according to previous study. Implementation aspects are thoroughly discussed. Finally, some numerical examples are provided, which are in agreement with our theoretical results.