Tomás Barrios, Rommel Bustinza, Camila Campos:
A note on a posteriori error estimates for dual mixed methods
In this paper, we describe a technique to develop an a posteriori error estimator for the dual mixed methods when applied to elliptic partial differential equations, with Dirichlet and mixed boundary conditions. The approach considers conforming finite elements for the discrete scheme and a quasi Helmholtz decomposition, to deduce an estimator of residual type. We prove its equivalence with the norm of the error, that is, reliability and local efficiency, without requiring the standard additional elliptic regularity on the boundary data. Numerical results are in agreement with the developed theory.
This preprint gave rise to the following definitive publication(s):
Tomás BARRIOS, Rommel BUSTINZA, Camila CAMPOS: An a posteriori error estimator for a non homogeneous Dirichlet problem considering a dual mixed formulation. Trends in Computational and Applied Mathematics, vol. 23, Issue 3, pp. 549-568 (2022).