Remarks on the analysis of finite element methods on a Shishkin mesh: are Scott-Zhang interpolants applicable?
نویسنده
چکیده
In the first part of the paper we discuss minimal smoothness assumptions for the components of the solution decomposition which allow to prove robust convergence results in the energy norm for linear or bilinear finite elements on Shishkin meshes applied to convectiondiffusion problems with exponential boundary layers. In the corresponding derivation the standard Lagrange interpolant is used, in general. In the second part we discuss the question whether or not it is possible to use the Scott-Zhang interpolant. AMS subject classification: 65N30
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تاریخ انتشار 2008