Multidimensional Extrapolation over Interfaces with Kinks and Regions of High Curvatures
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We present a PDE-based approach for the multidimensional extrapolation of smooth scalar quantities across interfaces with kinks and regions of high curvature. Second- and third-order accurate extensions in the L^∞ norm are obtained with linear and quadratic extrapolations, respectively. The accuracy of the method is demonstrated on a number of examples in two and three spatial dimensions and compared to the commonly used approach of [2]. Application of the method in the context of adaptive Quad-/Oc-tree grids is briefly discussed.
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