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

Asner, Liya; Tavener, Simon; Kay, David

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

Type

Article

Authors

Asner, Liya
Tavener, Simon
Kay, David

KAUST Grant Number

KUK-C1-013-04

Date

2012-01

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.

Citation

Asner L, Tavener S, Kay D (2012) Adjoint-Based a Posteriori Error Estimation for Coupled Time-Dependent Systems. SIAM Journal on Scientific Computing 34: A2394–A2419. Available: http://dx.doi.org/10.1137/110858458.

Acknowledgements

This work was supported in part by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).The first author's work is supported by the Clarendon Fund, University of Oxford, and by the Scatcherd European Scholarship.