Premium
Pointwise superconvergence of the streamline diffusion finite‐element method
Author(s) -
Zhou Guohui,
Rannacher Rolf
Publication year - 1996
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199601)12:1<123::aid-num7>3.0.co;2-u
Subject(s) - superconvergence , pointwise , convection–diffusion equation , mathematics , finite element method , polygon mesh , diffusion , scalar (mathematics) , pointwise convergence , convergence (economics) , convection , mathematical analysis , geometry , mechanics , computer science , physics , thermodynamics , approx , economics , economic growth , operating system
In this article, we analyze the local superconvergence property of the streamline‐diffusion finite‐element method (SDFEM) for scalar convection‐diffusion problems with dominant convection. By orienting the mesh in the streamline direction and imposing a uniformity condition on the mesh, the theoretical order of pointwise convergence is increased from O ( h 11/8 |log h |) to O ( h 2 |log h |). Numerical tests show that this result cannot be extended to arbitrary quasi‐uniform meshes. © 1996 John Wiley & Sons, Inc.