A primal-dual finite element method for transport equations in non-divergence form

This article presents a new primal-dual weak Galerkin (PDWG) finite element method for transport equations in non-divergence form. The PDWG method employs locally reconstructed differential operators and stabilizers in the weak Galerkin framework, and yields a symmetric discrete linear system involving the primal variable and the dual variable (known as the Lagrangian multiplier) for the adjoint equation. Optimal order error estimates are established in various discrete Sobolev norms for the corresponding numerical solutions. Numerical results are reported to illustrate the accuracy and efficiency of the new PDWG method. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This article presents a new primal-dual weak Galerkin (PDWG) finite element method for solving transport equations in non-divergence form. The method employs locally reconstructed differential operators and stabilizers in the weak Galerkin framework, and results in a symmetric discrete linear system involving the primal variable and the dual variable (Lagrangian multiplier) for the adjoint equation. The article establishes optimal order error estimates in various discrete Sobolev norms for the corresponding numerical solutions, and provides numerical results to demonstrate the accuracy and efficiency of the new PDWG method.