A Guide To The Finite And Virtual Element Methods For Elasticity

We present a systematic description and comparison of the Finite Element Method (FEM) with the relatively new Virtual Element Method (VEM) for solving boundary value problems in linear elasticity, including primal and mixed formulations. The description highlights the common base and the essential difference between FEM and VEM: discretisation of the same primal (Galerkin) and mixed weak formulations and assembly of element-wise quantities, but different approaches to element shape functions. The mathematical formulations are complemented with detailed description of the computer implementation of all methods, including all versions of VEM, which will benefit readers willing to develop their own computational framework. Numerical solutions of several boundary value problems are also presented in order to discuss the weaker and stronger sides of the methods. (c) 2021 The Authors. Published by Elsevier B.V. on behalf of IMACS. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).