Year: 2008
Numerical Mathematics: Theory, Methods and Applications, Vol. 1 (2008), Iss. 4 : pp. 383–409
Abstract
A class of normal-like derivatives for functions with low regularity defined on Lipschitz domains are introduced and studied. It is shown that the new normal-like derivatives, which are called the generalized normal derivatives, preserve the major properties of the existing standard normal derivatives. The generalized normal derivatives are then applied to analyze the convergence of domain decomposition methods (DDMs) with nonmatching grids and discontinuous Galerkin (DG) methods for second-order elliptic problems. The approximate solutions generated by these methods still possess the optimal energy-norm error estimates, even if the exact solutions to the underlying elliptic problems admit very low regularities.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-NMTMA-6056
Numerical Mathematics: Theory, Methods and Applications, Vol. 1 (2008), Iss. 4 : pp. 383–409
Published online: 2008-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Green's formula generalized normal derivative domain decomposition nonmathing grids discontinuous Galerkin error estimates.