Low Regularity Primal-Dual Weak Galerkin Finite Element Methods for Convection-Diffusion Equations

2019/01/20 by Chunmei Wang, Ludmil Zikatanov, Wang, Chunmei +1 · 2 citations
Engineering · Computer Science · #Advanced Numerical Methods in Computational Mathematics #Advanced Mathematical Modeling in Engineering #Computational Fluid Dynamics and Aerodynamics

paper · pdf · doi:10.48550/arxiv.1901.06743

Abstract

We propose a numerical method for convection-diffusion problems under low regularity assumptions. We derive the method and analyze it using the primal-dual weak Galerkin (PDWG) finite element framework. The Euler-Lagrange formulation resulting from the PDWG scheme yields a system of equations involving not only the equation for the primal variable but also its adjoint for the dual variable. We show that the proposed PDWG method is stable and convergent. We also derive a priori error estimates for the primal variable in the H^ε-norm for ε∈ [0,\frac12). A series of numerical tests that validate the theory and are presented as well.

Citations

• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

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