Robust a Posteriori Error Control and Adaptivity for Multiscale, Multinumerics, and Mortar Coupling

Gergina V. Pencheva, Martin Vohralík, Mary F. Wheeler, Tim Wildey

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

We consider discretizations of a model elliptic problem by means of different numerical methods applied separately in different subdomains, termed multinumerics, coupled using the mortar technique. The grids need not match along the interfaces. We are also interested in the multiscale setting, where the subdomains are partitioned by a mesh of size h, whereas the interfaces are partitioned by a mesh of much coarser size H, and where lower-order polynomials are used in the subdomains and higher-order polynomials are used on the mortar interface mesh. We derive several fully computable a posteriori error estimates which deliver a guaranteed upper bound on the error measured in the energy norm. Our estimates are also locally efficient and one of them is robust with respect to the ratio H/h under an assumption of sufficient regularity of the weak solution. The present approach allows bounding separately and comparing mutually the subdomain and interface errors. A subdomain/interface adaptive refinement strategy is proposed and numerically tested. © 2013 Society for Industrial and Applied Mathematics.
Original languageEnglish (US)
Pages (from-to)526-554
Number of pages29
JournalSIAM Journal on Numerical Analysis
Volume51
Issue number1
DOIs
StatePublished - Jan 2013
Externally publishedYes

Fingerprint

Dive into the research topics of 'Robust a Posteriori Error Control and Adaptivity for Multiscale, Multinumerics, and Mortar Coupling'. Together they form a unique fingerprint.

Cite this