Aufsatz in einer Fachzeitschrift
Duality and finite elements
Details zur Publikation
Autor(inn)en: | Grätsch, T.; Hartmann, F. |
Publikationsjahr: | 2004 |
Zeitschrift: | Finite Elements in Analysis and Design: An International Journal for Innovations in Computational Methodology and Application |
Seitenbereich: | 1005-1020 |
Jahrgang/Band : | 40 |
ISSN: | 0168-874X |
eISSN: | 1872-6925 |
DOI-Link der Erstveröffentlichung: |
Zusammenfassung, Abstract
Post-processing in finite element analysis is essentially based on duality techniques: nodal values and point values in general or integrals of stresses are obtained by employing influence functions involving appropriate kernel functions G(i)(h)(y, x) which are the projections of the exact kernel functions G(i)(y, x) onto the trial space V-h. Duality is therefore, as we want to show, a key concept of finite element methods. Questions of accuracy as well as questions of global and local equilibrium can be answered in this context. To this end we first formulate an Equivalence Theorem which establishes the connection between the finite element solution and the exact solution via Green's first identity. We next show that post-processing is essentially an application of Green's first or second identity. Finally, we formulate a new Projection Theorem which encapsulates the whole theory. (C) 2003 Elsevier B.V. All rights reserved.
Post-processing in finite element analysis is essentially based on duality techniques: nodal values and point values in general or integrals of stresses are obtained by employing influence functions involving appropriate kernel functions G(i)(h)(y, x) which are the projections of the exact kernel functions G(i)(y, x) onto the trial space V-h. Duality is therefore, as we want to show, a key concept of finite element methods. Questions of accuracy as well as questions of global and local equilibrium can be answered in this context. To this end we first formulate an Equivalence Theorem which establishes the connection between the finite element solution and the exact solution via Green's first identity. We next show that post-processing is essentially an application of Green's first or second identity. Finally, we formulate a new Projection Theorem which encapsulates the whole theory. (C) 2003 Elsevier B.V. All rights reserved.
