20090205
Anisotropic mesh adaptation has proven to be a useful tool for enhancing accuracy and efficacy in the numerical solution of partial differential equations, especially those exhibiting anisotropic features in their solutions and/or structures. On the other hand, the mathematical characterization of anisotropic meshes has not been well understood. In this talk I will present an approach with which anisotropic meshes are viewed as uniform ones in some metric space. An advantage of this approach is that the simple characterization of uniform meshes will lead to a clear mathematical characterization of adaptive, often nonuniform meshes. As a result, two conditions, the wellknown equidistribution condition and a lessknown alignment one, are shown to be able to characterize the size and the shape and orientation of elements of anisotropic meshes, respectively.
Applications of the characterization to anisotropic mesh generation and error analysis in finite element computation will be discussed. Numerical examples and applications will be given.
Category: CE SeminarTechnische Universität Darmstadt
Graduate School CE
Dolivostraße 15
D64293 Darmstadt

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