A VEM–based mesh–adaptive strategy for potential problems

[Annamaria Mazzia, Flavio Sartoretto] Volume 6: Issue 1, March 2019, pp  

DOI: 10.26706/IJAEFEA.1.6.20190301

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Abstract The Virtual Element Method (VEM) is an evolution of the mimetic finite difference method which overcomes many lim- itations affecting classic Finite Element Methods (FEM). VEM for 2D problems allows for exploiting meshes consist- ing of any polygonal elements.  No limitations on their in- ternal angles are needed. Hanging nodes are easily treated. Notably, VEM is well apt to mesh–adaptive algorithms. In this paper we detail an implementation of mesh–adaptive VEM for potential problems.  We suggest a fresh, promis- ing approach.  We show on suitable test problems that a gain in efficiency can be obtained, respect to uniform, fine discretizations.

Index terms - VEM,  Mesh  Adaptivity,  Poisson Problem.
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