A nonlinear weak constraint enforcement method for advection-dominated diffusion problems

TL;DR

This paper introduces a stabilized numerical method that weakly enforces bound constraints in advection-dominated diffusion problems, combining nonlinear penalties with residual minimization for improved accuracy on various meshes.

Contribution

The paper presents a novel stabilized approach integrating nonlinear penalty and residual minimization for bound constraint enforcement in advection-dominated diffusion problems.

Findings

Effective enforcement of bound constraints demonstrated on uniform meshes

Adaptive mesh performance shown to be robust and accurate

Method outperforms traditional approaches in numerical examples

Abstract

We devise a stabilized method to weakly enforce bound constraints in the discrete solution of advection-dominated diffusion problems. This method combines a nonlinear penalty formulation with a discontinuous Galerkin-based residual minimization method. We illustrate the efficiency of this scheme for both uniform and adaptive meshes through proper numerical examples.