Anisotropic Adaption and Structure Detection

Abstract

In this paper, we suggest a general approach of an anisotropic adaption procedure in the context of numerical schemes for hyperbolic conservation laws. This approach consists of coupling a structure detection tool from image processing with a new, non-iterative anisotropic adaption algorithm. Ingo Thomas Inst. f. Angew. Math. Bundesstr. 55 20146 Hamburg [email protected] August 20, 1999 Contents 1 Anisotropic Adaption 4 1.1 Representation of an anisotropic grid resolution by symmetric positive definite matrices . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Discrete interpretation of the anisotropic refinement information 4 1.3 Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Isotropic Adaption 7 3 Anisotropic Adaption 8 3.1 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 First Step: Splitting of edges . . . . . . . . . . . . . . . ...