Stabilized finite elements on anisotropic meshes: A priori error estimates for the advection-diffusion and the Stokes problems
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 a. ne mapping from the reference 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 h(K) but on a characteristic length associated with K via the polar decomposition. A numerical assessment of the theoretical analysis is carried out.
Keywords: anisotropic error estimates ; advection-diffusion problems ; Stokes ; problem ; stabilized finite elements ; COMPUTATIONAL FLUID-DYNAMICS ; LEAST-SQUARES METHODS ; INCOMPRESSIBLE ; FLOWS ; EQUATIONS ; FORMULATION ; APPROXIMATION ; REFINEMENT
Politecn Milan, MOX Modeling & Sci Comp, Dipartimento Matemat F Brioschi, I-20133 Milan, Italy. Ecole Polytech Fed Lausanne, Inst Math, CH-1015 Lausanne, Switzerland. Micheletti, S, Politecn Milan, MOX Modeling & Sci Comp, Dipartimento Matemat F Brioschi, Via Bonardi 9, I-20133 Milan, Italy.
ISI Document Delivery No.: 718DU
Times Cited: 5
Cited Reference Count: 41
Record created on 2006-08-24, modified on 2016-08-08