Rommel Bustinza, Jonathan Munguia:
An HHO formulation for a Neumann problem on general meshes
In this work, we study a Hybrid High-Oder (HHO) method for an elliptic diffusion problem with Neumann boundary condition. The proposed method has several features, such as: i) the support of arbitrary approximation order polynomial at mesh elements and faces on general polyhedral meshes, ii) the design of a local (element-wise) discrete gradient reconstruction operator and a local stabilization term, that weakly enforces the matching between local element- and face- based on degrees of Freedom (DOF), and iii) 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 . Implementation aspects are throughly discussed. Finally, some numerical examples are provided, which are in agreement with our theoretical results.
This preprint gave rise to the following definitive publication(s):
Rommel BUSTINZA, Jonathan MUNGUIA: A hybrid high-order formulation for a Neumann problem on polytopal meshes. Numerical Methods for Partial Differential Equations, vol. 36, 3, pp. 524-551 (2020).