Using the de Rham sequence for accelerating mixed finite element computations

Resumo

Mixed finite element computations arise in the simulation of multiple physical phenomena. Due to its

characteristics, such as the strong coupling between the approximated variables, the solution of such class of prob-
lems may suffer from numerical instabilities as well as a computational cost. The de Rham diagram is a standard

tool to provide approximation spaces for the solution of mixed problems as it relates H1

-conforming spaces with
H(curl) and H(div)-conforming elements in a simple way by means of differential operators. This work presents
an alternative for accelerating the computation of mixed problems by exploring the de Rham sequence to derive
divergence-free functions in a robust fashion. The formulation is numerically verified for the 2D case by means of
benchmark cases to confirm the theoretical regards.