NDLI: Stabilized Finite Elements on Anisotropic Meshes: A Priori Error Estimates for the Advection-Diffusion and the Stokes Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Perotto, Simona Picasso, Marco Micheletti, Stefano
Copyright Year	2003
Abstract	Stabilized finite elements on strongly anisotropic meshes are considered. The design of the stability coefficients is addressed for both the advection-diffusion and the Stokes problems when using continuous piecewise linear finite elements on triangles. Using the polar decomposition of the Jacobian of the affine mapping from thereference triangle to the current one, K, and from a priori error estimates, a new definition of the stability coefficients is proposed. Our analysis shows that these coefficients do not depend on the element diameter hK but on a characteristic length associated with K via the polar decomposition. A numerical assessment of the theoretical analysis is carried out.
Starting Page	1131
Ending Page	1162
Page Count	32
File Format	PDF
ISSN	00361429
DOI	10.1137/S0036142902403759
e-ISSN	10957170
Issue Number	3
Volume Number	41
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-26
Access Restriction	Subscribed
Subject Keyword	Stability and convergence of numerical methods Stokes problem advection-diffusion problems Error bounds stabilized finite elements Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods anisotropic error estimates
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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