Stabilization and a posteriori error analysis of a mixed FEM for convection-diffusion problems with mixed boundary conditions

Tipo de publicación
Artículo en revista
Autores

María Gonzalez, Magdalena Strugaru

 

Abstract


We introduce a new augmented dual-mixed finite element method for the linear convection-diffusion equation with mixed boundary conditions. The approach is based on adding suitable residual type terms to a dual-mixed formulation of the problem. We prove that for appropriate values of the stabilization parameters, that depend on the diffusivity and the magnitude of the convective velocity, the new variational formulation and the corresponding Galerkin scheme are well-posed and a Céa estimate can be derived. We establish the rate of convergence when the flux and the concentration are approximated, respectively, by Raviart–Thomas/Brezzi–Douglas–Marini and continuous piecewise polynomials. In addition, we develop an a posteriori error analysis of residual type. We derive a simple a posteriori error indicator and prove that it is reliable and locally efficient. Finally, we provide some numerical experiments that illustrate the performance of the method.

Editor
ScienceDirect ®
Año de publicación
2021
Lugar de publicación
https://www.sciencedirect.com/science/article/pii/S037704272030306X?via%3Dihub
Cita bibliográfica

María González, Magdalena Strugaru, Stabilization, and a posteriori error analysis of a mixed FEM for convection-diffusion problems with mixed boundary conditions, Journal of Computational and Applied Mathematics, Volume 381, 2021, 113015, ISSN 0377-0427, https://doi.org/10.1016/j.cam.2020.113015.

DOI
https://doi.org/10.1016/j.cam.2020.113015