Adjoint-Based a Posteriori Error Estimation for Coupled Time-Dependent Systems

Liya Asner, Simon Tavener, David Kay

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We consider time-dependent parabolic problem s coupled across a common interface which we formulate using a Lagrange multiplier construction and solve by applying a monolithic solution technique. We derive an adjoint-based a posteriori error representation for a quantity of interest given by a linear functional of the solution. We establish the accuracy of our error representation formula through numerical experimentation and investigate the effect of error in the adjoint solution. Crucially, the error representation affords a distinction between temporal and spatial errors and can be used as a basis for a blockwise time-space refinement strategy. Numerical tests illustrate the efficacy of the refinement strategy by capturing the distinctive behavior of a localized traveling wave solution. The saddle point systems considered here are equivalent to those arising in the mortar finite element technique for parabolic problems. © 2012 Society for Industrial and Applied Mathematics.
Original languageEnglish (US)
Pages (from-to)A2394-A2419
Number of pages1
JournalSIAM Journal on Scientific Computing
Volume34
Issue number4
DOIs
StatePublished - Jan 2012
Externally publishedYes

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