A hybrid high-order formulation for a Neumann problem on polytopal meshes |
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Authors: | Rommel Bustinza Jonathan Munguia-La-Cotera |
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Institution: | 1. Departamento de Ingeniería Matemática and Centro de Investigación en Ingeniería Matemática (CI2MA), Universidad de Concepción, Concepción, Chile;2. Instituto de Matemática y Ciencias Afines (IMCA), Lima, Perú
Escuela Profesional de Matemática, Facultad de Ciencias, Universidad Nacional de Ingeniería, Lima, Perú |
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Abstract: | 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. |
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Keywords: | a priori error estimate hybrid high order method polytopal mesh reconstruction operator |
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