Year: 2019
Type: article
Abstract: We consider primal dual mixed finite element methods for the advection-diffusion equation. For the primal variable we use standard continuous finite element space and for the flux we use the Raviart-Thomas space. We prove optimal a priori error estimates in the $H^1$- and the $L^2$-norms for the primal variable in the low Péclet regime. In the high Péclet regime we also prove optimal error estimates for the primal variable in the $H(div)$ norm for smooth solutions. Numerically we observe that the method eliminates the spurious oscillations close to interior layers that pollute the solution of the standard Galerkin method when the local Péclet number is high. This method, however, does produce spurious oscillations when outflow boundary layers are present in the solution. In the last section we propose two simple strategies to remove such numerical artifacts caused by the outflow boundary layer and validate them numerically.
DOI: 10.1137/18m1221473
Authors: Erik Burman, Cuiyu He
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2898892744