Deviation identity for linear differential operators and its application to obstacle problems

TL;DR

This paper introduces a deviation identity for linear differential operators in variational problems, providing a practical way to measure the distance between approximate and exact solutions, with applications to obstacle problems.

Contribution

It develops a new deviation identity for linear differential operators and applies it explicitly to biharmonic obstacle problems.

Findings

Explicit deviation identity for biharmonic obstacle problem

Provides a practical tool for estimating solution accuracy

Enhances understanding of approximation errors in variational problems

Abstract

For a class of variational problems with linear differential operator, we obtain a convenient form of the deviation identity, i.e., the value of the distance between approximated solutions and the exact ones. We illustrate the result with an explicit form of the deviation identity for a biharmonic obstacle problem.