Functional a posteriori error estimates for parabolic obstacle problems

TL;DR

This paper develops guaranteed, computable a posteriori error estimates for parabolic obstacle problems, enabling precise assessment of approximation errors and modeling inaccuracies in numerical solutions.

Contribution

It introduces functional a posteriori error bounds for parabolic obstacle problems, including applications to data simplification and time incremental approximations.

Findings

Effective error bounds demonstrated through numerical examples

Application to modeling errors due to data simplification

Special focus on time incremental approximation methods

Abstract

The paper is concerned with functional type a posteriori estimates for the initial boundary value problem for a parabolic partial differential equation with an obstacle. We deduce a guaranteed and computable bound of the distance between the exact minimizer and any function from the admissible (energy) class of functions. Applications to the analysis of modeling errors caused by data implification are discussed. An important case of time incremental approximations is specially studied. Numerical examples presented in the last section show how the estimates work in practice.