Jump to Content
Your Recent History
View Cart
Logged Out Log In
SIAM J. Sci. Comput. 34, pp. A497-A519 (23 pages)
Solving Dirichlet Boundary-value Problems on Curved Domains by Extensions from Subdomains
Alerts
Alert Me When Cited
Alert Me When Corrected
Tools
Download Citation
Add to MyScitation
Blog This Article
Print-Friendly
Research Toolkit
Share
Email Abstract
Connotea
CiteULike
del.icio.us
BibSonomy
Tweet this Article
Add to FacebookWe present a technique for numerically solving Dirichlet boundary-value problems for second-order elliptic equations on domains $\Omega$ with curved boundaries. This is achieved by using suitably defined extensions from polyhedral subdomains $\textsf{D}_h$; the problem of dealing with curved boundaries is thus reduced to the evaluations of simple line integrals. The technique is independent of the representation of the boundary, of the space dimension, and allows for the use of only polyhedral elements. We apply this technique to the hybridizable discontinuous Galerkin method and provide extensive numerical experiments showing that the convergence properties of the resulting method are the same as those for the case in which $\Omega=\textsf{D}_h$ whenever the distance of $\textsf{D}_h$ to $\partial\Omega$ is of order $h$. In particular, we find that when using polynomial approximations of degree $k$ on the polyhedral subdomains $\textsf{D}_h$, both the scalar and vector unknowns converge with the optimal order of $k+1$ in the whole domain $\Omega$ for $k\ge0$. Moreover, we also find that for $k\ge1$, both a postprocessing of the scalar unknown in the polyhedral subdomain $\textsf{D}_h$ as well as its extension from it converge with order $k+2$. The extension also converges with order $2$ for $k=0$.
© 2012 Society for Industrial and Applied Mathematics
RELATED DATABASES
To view database links for this article,
you need to log in.
KEYWORDS
Keywords
curved domains, immersed boundary methods, discontinuous Galerkin methods, elliptic equationsAMS Subject Headings
65N30PUBLICATION DATA
ARTICLE DATA
History
Received August 13, 2010
Accepted October 28, 2011
Published online February 14, 2012
Accepted October 28, 2011
Published online February 14, 2012
Digital Object Identifier
For access to fully linked references, you need to log in.
ALL SIAM Content
Scitation
Google Scholar