$L^\infty$ bounds for numerical solutions of noncoercive convection-diffusion equations

TL;DR

This paper develops an iterative energy method inspired by de Giorgi to establish $L^{ obreakinfty}$ bounds for numerical solutions of noncoercive convection-diffusion equations with mixed boundary conditions, enhancing stability analysis.

Contribution

It introduces a novel application of de Giorgi's iterative energy method to obtain $L^{ obreakinfty}$ bounds for noncoercive convection-diffusion equations in a numerical setting.

Findings

Established $L^{ obreakinfty}$ bounds for numerical solutions.

Extended energy methods to noncoercive PDEs.

Addressed mixed boundary conditions in stability analysis.

Abstract

In this work, we apply an iterative energy method \`a la de Giorgi in order to establish $L^{\infty}$ bounds for numerical solutions of noncoercive convection-diffusion equations with mixed Dirichlet-Neumann boundary conditions.