Error analysis of finite element approximations of diffusion coefficient identification for elliptic and parabolic problems

Bangti Jin, Zhi Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

In this work, we present a novel error analysis for recovering a spatially dependent diffusion coefficient in an elliptic or parabolic problem. It is based on the standard regularized output least-squares formulation with an H1(Ω) seminorm penalty and then discretized using the Galerkin finite element method with conforming piecewise linear finite elements for both state and coefficient and backward Euler in time in the parabolic case. We derive a priori weighted L2(Ω ) estimates where the constants depend only on the given problem data for both elliptic and parabolic cases. Further, these estimates also allow deriving standard L2(Ω ) error estimates under a positivity condition that can be verified for certain problem data. Numerical experiments are provided to complement the error analysis.

Original languageEnglish
Pages (from-to)119–142
Number of pages24
JournalSIAM Journal on Numerical Analysis
Volume59
Issue number1
Early online dateJan 2021
DOIs
Publication statusPublished - Feb 2021

Keywords

  • Error estimate
  • Finite element approximation
  • Parameter identification
  • Tikhonov regularization

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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