Permanent URL to this publication: http://dx.doi.org/10.5167/uzh21787
Dahmen, W; Faermann, B; Graham, I; Hackbusch, W; Sauter, S (2004). Inverse inequalities on nonquasiuniform meshes and application to the mortar element method. Mathematics of Computation, 73(247):11071138 (electronic).

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Abstract
We present a range of meshdependent inequalities for piecewise constant and continuous piecewise linear finite element functions u defined on locally refined shaperegular (but possibly nonquasiuniform) meshes. These inequalities involve norms of the form ∥h α u∥ W s,p (Ω) for positive and negative s and α, where h is a function which reflects the local mesh diameter in an appropriate way. The only global parameter involved is N, the total number of degrees of freedom in the finite element space, and we avoid estimates involving either the global maximum or minimum mesh diameter.
Our inequalities include new variants of inverse inequalities as well as trace and extension theorems. They can be used in several areas of finite element analysis to extend results – previously known only for quasiuniform meshes – to the locally refined case. Here we describe applications to (i) the theory of nonlinear approximation and (ii) the stability of the mortar element method for locally refined meshes.
Item Type:  Journal Article, refereed, original work 

Communities & Collections:  07 Faculty of Science > Institute of Mathematics 
DDC:  510 Mathematics 
Uncontrolled Keywords:  Inequalities, meshdependent norms, inverse estimates, nonlinear approximation theory, nonmatching grids, mortar element method, boundary element method 
Language:  English 
Date:  2004 
Deposited On:  29 Nov 2010 16:26 
Last Modified:  27 Nov 2012 13:02 
Publisher:  American Mathematical Society 
ISSN:  00255718 
Additional Information:  First published in [Math. Comp. 73 (2004), no. 247], published by the American Mathematical Society 
Publisher DOI:  10.1090/S0025571803015837 
Related URLs:  http://www.ams.org/mathscinetgetitem?mr=2047080 
Citations:  Google Scholar™ Scopus®. Citation Count: 14 
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