A priori and a posteriori error analyses of an HDG method for the Brinkman problem. (15th February 2018)

• Record Type: Journal Article
• Authors: Gatica, Luis F.; Sequeira, Filánder A.
• Is Part Of: Computers & mathematics with applications. Volume 75:issue 4(2018)
• Page Start: 1191
• Page End: 1212
• Publication Date: 2018-02-15
• Subjects: Linear Brinkman model -- Hybridized discontinuous Galerkin method -- A posteriori error analysis -- Postprocessed techniques -- High-order approximations; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.10.038
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper we introduce and analyze a hybridizable discontinuous Galerkin (HDG) method for the linear Brinkman model of porous media flow in two and three dimensions and with non-homogeneous Dirichlet boundary conditions. We consider a fully-mixed formulation in which the main unknowns are given by the pseudostress, the velocity and the trace of the velocity, whereas the pressure is easily recovered through a simple postprocessing. We show that the corresponding continuous and discrete schemes are well-posed. In particular, we use the projection-based error analysis in order to derive a priori error estimates. Furthermore, we develop a reliable and efficient residual-based a posteriori error estimator, and propose the associated adaptive algorithm for our HDG approximation. Finally, several numerical results illustrating the performance of the method, confirming the theoretical properties of the estimator and showing the expected behavior of the adaptive refinements are presented.