2004-03-02Buch DOI: 10.18452/2556
A Unifying Theory Of A Posteriori Finite Element Error Control
 dc.contributor.author Carstensen, Carsten dc.date.accessioned 2017-06-15T17:32:33Z dc.date.available 2017-06-15T17:32:33Z dc.date.created 2005-11-02 dc.date.issued 2004-03-02 dc.identifier.issn 0863-0976 dc.identifier.uri http://edoc.hu-berlin.de/18452/3208 dc.description.abstract Residual-based a posteriori error estimates are derived wihtin a unified setting for lowest-order conforming, nonconforming, and mixed finite element schemes. The various residuals are identified for all techniques and problems as the operator norm $\| l \|$ of a linear functional of the form $l(v) := \int_{\Omega} p_h : Dv dx + \int_{\Omega} g_{\Omega} \cdot v dx$ in the variable $v$ of a Soboloev space $V$. The main assumption is that the first-order finite element space $S^1_0 (\Omega) \subset \ker l \subset V$ is included in the kernel $\ker l$ of $l$. As a consequence, {\it any residual estimator} that is a computable bound of $\| l \|$ can be used within the proposed frame {\it without} further analysis for nonconforming or mixed FE schemes. Applications are given for the Laplace, Stokes, and Navier-Lam\'e equations. eng dc.language.iso eng dc.publisher Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik dc.rights.uri http://rightsstatements.org/vocab/InC/1.0/ dc.subject finite element method eng dc.subject A posteriori eng dc.subject error analysis eng dc.subject nonconforming finite element method eng dc.subject mixed finite element method eng dc.subject adaptive algorithm eng dc.subject.ddc 510 Mathematik dc.title A Unifying Theory Of A Posteriori Finite Element Error Control dc.type book dc.identifier.urn urn:nbn:de:kobv:11-10051766 dc.identifier.doi http://dx.doi.org/10.18452/2556 local.edoc.pages 21 local.edoc.type-name Buch local.edoc.container-type series local.edoc.container-type-name Schriftenreihe local.edoc.container-year 2005 dc.identifier.zdb 2075199-0 bua.series.name Preprints aus dem Institut für Mathematik bua.series.issuenumber 2005,5