Estimates of the distance to the exact solution of parabolic problems based on local Poincar\'e type inequalities

TL;DR

This paper develops two-sided bounds for the distance between the exact solution of a reaction-diffusion problem and any admissible function, using local Poincaré inequalities to improve error estimation in parabolic PDEs.

Contribution

It introduces novel two-sided bounds based on local Poincaré inequalities for estimating the solution's accuracy in reaction-diffusion problems.

Findings

Derived explicit two-sided bounds for solution approximation errors

Applied local Poincaré inequalities to reaction-diffusion problems

Enhanced error estimation techniques for parabolic PDEs

Abstract

The goal of the paper is to derive two-sided bounds of the distance between the exact solution of the evolutionary reaction-diffusion problem with mixed Dirichlet--Robin boundary conditions and any function in the admissible energy space.