Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Projection methods for Dirichlet's problem in approximating polygonal domains with boundary-value corrections


Authors: James H. Bramble, Todd Dupont and Vidar Thomée
Journal: Math. Comp. 26 (1972), 869-879
MSC: Primary 65N30
MathSciNet review: 0343657
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Consider Dirichlet's problem in a plane domain $ \Omega $ with smooth boundary $ \partial \Omega $. For the purpose of its approximate solution, an approximating domain $ {\Omega _h},0 < h \leqq 1$, with polygonal boundary $ \partial {\Omega _h}$ is introduced where the segments of $ \partial {\Omega _h}$ have length at most $ h$. A projection method introduced by Nitsche [6] is then applied on $ {\Omega _h}$ to give an approximate solution in a finite-dimensional subspace of functions $ {S_h}$, for instance a space of splines defined on a triangulation of $ {\Omega _h}$. The boundary terms in the bilinear form associated with Nitsche's method are modified to correct for the perturbation of the boundary.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N30

Retrieve articles in all journals with MSC: 65N30


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1972-0343657-7
PII: S 0025-5718(1972)0343657-7
Article copyright: © Copyright 1972 American Mathematical Society