Comparing Lagrange and Mixed finite element methods using MFEM library

TL;DR

This paper develops and compares two finite element formulations for the Laplace problem using the MFEM library, analyzing their equivalence and performance across different mesh refinements and shape function orders.

Contribution

It introduces two finite element formulations for Laplace, demonstrates their equivalence, and provides a comparative analysis using the MFEM library.

Findings

The two formulations are equivalent under certain conditions.

Solution accuracy varies with shape function order and mesh refinement.

MFEM library effectively supports finite element analysis for Laplace problems.

Abstract

In this paper, we develop two finite element formulations for the Laplace problem and find the way in which they are equivalent. Then we compare the solutions obtained by both formulations, by changing the order of the shape functions and the refinement level of the mesh (star with rhomboidal elements). And, we will give an overview of MFEM library from the LLNL (Lawrence Livermore National Laboratory), as it is the library used to obtain the solutions.