Adjoint Based A Posteriori Analysis of Multiscale Mortar Discretizations with Multinumerics

Simon Tavener, Tim Wildey

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper we derive a posteriori error estimates for linear functionals of the solution to an elliptic problem discretized using a multiscale nonoverlapping domain decomposition method. The error estimates are based on the solution of an appropriately defined adjoint problem. We present a general framework that allows us to consider both primal and mixed formulations of the forward and adjoint problems within each subdomain. The primal subdomains are discretized using either an interior penalty discontinuous Galerkin method or a continuous Galerkin method with weakly imposed Dirichlet conditions. The mixed subdomains are discretized using Raviart- Thomas mixed finite elements. The a posteriori error estimate also accounts for the errors due to adjoint-inconsistent subdomain discretizations. The coupling between the subdomain discretizations is achieved via a mortar space. We show that the numerical discretization error can be broken down into subdomain and mortar components which may be used to drive adaptive refinement.Copyright © by SIAM.
Original languageEnglish (US)
Pages (from-to)A2621-A2642
Number of pages1
JournalSIAM Journal on Scientific Computing
Volume35
Issue number6
DOIs
StatePublished - Jan 2013
Externally publishedYes

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