An H^1-conforming Virtual Element Method for Darcy equations and Brinkman equations
Abstract
The focus of the present paper is on developing a Virtual Element Method for Darcy and Brinkman equations. In [15] we presented a family of Virtual Elements for Stokes equations and we defined a new Virtual Element space of velocities such that the associated discrete kernel is pointwise divergence-free. We use a slightly different Virtual Element space having two fundamental properties: the L^2-projection onto P_k is exactly computable on the basis of the degrees of freedom, and the associated discrete kernel is still pointwise divergence-free. The resulting numerical scheme for the Darcy equation has optimal order of convergence and H^1 conforming velocity solution. We can apply the same approach to develop a robust virtual element method for the Brinkman equation that is stable for both the Stokes and Darcy limit case. We provide a rigorous error analysis of the method and several numerical tests.
Cite
@article{arxiv.1701.07680,
title = {An H^1-conforming Virtual Element Method for Darcy equations and Brinkman equations},
author = {Giuseppe Vacca},
journal= {arXiv preprint arXiv:1701.07680},
year = {2017}
}
Comments
arXiv admin note: text overlap with arXiv:1510.01655