Low regularity primal-dual weak Galerkin finite element methods for convection-diffusion equations (Q2029419)

The standard Galerkin finite element approximation mostly exhibit nonphysical oscillating solutions when applied to the convection-diffusion boundary value problems in convective dominating regime. The authors are concerned with the construction and analysis of primal-dual weak Galerkin (PDWG) stable solutions to such problems. In order to accomplish this aim they combine solutions of the primal and the dual (adjoint) equation, PDWG techniques being natural in deriving error estimates under low regularity assumptions. A critical inf-sup condition is used in order to derive error estimates in an optimal order for the primal-dual WG finite element method in some discrete Sobolev norms. Some numerical experiments are carried out to demonstrate the effectiveness and accuracy of the numerical method.