A discontinuous-skeletal method for advection-diffusion-reaction on general meshes

Abstract

We design and analyze an approximation method for advection-diffusion-reaction equations where the (generalized) degrees of freedom are polynomials of order $k\ge 0$ at mesh faces. The method hinges on local discrete reconstruction operators for the diffusive and advective derivatives and a weak enforcement of boundary conditions. Fairly general meshes with polytopal and nonmatching cells are supported. Arbitrary polynomial orders can be considered, including the case $k=0$ which is closely related to Mimetic Finite Difference/Mixed-Hybrid Finite Volume methods. The error analysis covers the full range of Péclet numbers, including the delicate case of local degeneracy where diffusion vanishes on a strict subset of the domain. Computational costs remain moderate since the use of face unknowns leads to a compact stencil with reduced communications. Numerical results are presented.

References in corpus (1)

• A Hybrid High-Order method for the incompressible Navier--Stokes equations based on Temam's device

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