Study of the enriched mixed finite element method using comparisons of computational cost and errors with formulations in continuous and discon- tinuous functions and mixed scheme on quadrilateral finite elements.

Resumo

Mixed finite element formulations are used to approximate stress and displacement variables simultane-
ously for Poisson problems. The purpose of this article is to analyze new discrete mixed approximation based on

the application of enriched version of classic Poisson-compatible spaces. With that purpose we decided to measure
the computational cost of applying four formulations for two Poisson problems with known exact solution. The

first model considers a smooth sinusoidal solution and the second model has a high gradient solution. The objec-
tive is not to compare which formulation is better, but rather to highlight characteristics of computational cost and

the errors obtained for both the primal and dual variables. Weak formulations correspond to the use of the FEM
using continuous and discontinuous functions, using the mixed method and the enrichment mixed method. In the
algorithms developed, we computed the error in L
2
and H1 norms and we measured the computational cost of the
assembly and solving processes. When analyzing these costs together with the errors obtained, we visualized that
the cost of enriched version is less expensive computationally than non-enriched version, however they getting the
same approximation errors.