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Application of the R‐functions method to the solution of elliptic PDEs (Poster Presentation)
Author(s) -
Gladkov Svyatoslav,
Svendsen Bob
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200701055
Subject(s) - biharmonic equation , mathematics , poisson's equation , norm (philosophy) , mathematical analysis , finite element method , dirichlet boundary condition , convergence (economics) , dirichlet problem , boundary value problem , physics , political science , law , economics , thermodynamics , economic growth
In the current work, the basics of the theory of R‐functions have been presented. Applications of this theory were shown on two model problems – Poisson equation and biharmonic equation – in complex two‐dimensional domains both with homogeneous Dirichlet boundary conditions. The solution is performed in conjunction with the Bubnov‐Galerkin method. As the basis for approximation tensor products of monomials were taken. The convergence study includes the comparison of current results with the standard finite element solution and the dependence of the number of coordinate functions on the relative error in the maximum‐norm. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)