Abstract:In this paper, we propose a positivity-preserving conservative scheme based on the virtual element method (VEM) to solve convection-diffusion problems on general meshes. As an extension of finite element methods to general polygonal elements, the VEM has many advantages such as substantial mathematical foundations, simplicity in implementation. However, it is neither positivity-preserving nor locally conservative. The purpose of this article is to develop a new scheme, which has the same accuracy as the VEM an… Show more
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