Premium
Pointwise error estimates of the bilinear SDFEM on Shishkin meshes
Author(s) -
Zhang Jin,
Mei Liquan
Publication year - 2013
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/num.21712
Subject(s) - mathematics , pointwise , piecewise , polygon mesh , finite element method , bilinear interpolation , convection–diffusion equation , boundary (topology) , partial differential equation , bilinear form , uniform convergence , space (punctuation) , mathematical analysis , geometry , computer science , computer network , statistics , physics , bandwidth (computing) , thermodynamics , operating system
A model singularly perturbed convection–diffusion problem in two space dimensions is considered. The problem is solved by a streamline diffusion finite element method (SDFEM) that uses piecewise bilinear finite elements on a Shishkin mesh. We prove that the method is convergent, independently of the diffusion parameter ε, with a pointwise accuracy of almost order 11/8 outside and inside the boundary layers. Numerical experiments support these theoretical results. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013