Mixed Finite Element Methods for the Poisson Equation Using Biorthogonal and Quasi-Biorthogonal Systems

Abstract EN

We introduce two three-field mixed formulations for the Poisson equation and propose finite element methods for their approximation.

Both mixed formulations are obtained by introducing a weak equation for the gradient of the solution by means of a Lagrange multiplier space.

Two efficient numerical schemes are proposed based on using a pair of bases for the gradient of the solution and the Lagrange multiplier space forming biorthogonal and quasi-biorthogonal systems, respectively.

We also establish an optimal a priori error estimate for both finite element approximations.