A semi-Lagrangian mixed finite element method for advection-diffusion variational inequalities

We present a computational methodology for solving advection-diffusion variational inequalities. Our method is based on a Lagrange-Galerkin technique which combines a discretization of the material derivative along particle trajectories with a mixed finite element method. An efficient primal-dual active-set algorithm is designed to solve the resulting saddle point complementarity system. The overall approach applies to both advection and diffusion-dominated problems, and its performance is demonstrated on numerical examples with known analytical solutions and a benchmark from the literature. (c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.