Comparison of the performance of some finite element discretizations for large deformation elasticity problems

In this paper, known analytical solutions are used to compare various finite element discretizations for the numerical solution of large deformation problems involving hyperelastic materials. This approach is also known as the method of manufactured solutions (MMS). The performance of these different discretizations is analyzed in terms of convergence in a suitable norm with respect to mesh size, and also in terms of computational cost and memory consumption. Some interesting features of mixed finite element discretizations are presented and discussed. The test cases presented can also serve as nontrivial benchmark problems and as a basis for code verification.