Abstract
Unlike other schemes that locally violate the essential stability properties of the analytic parabolic and elliptic problems, Voronoi finite volume methods (FVM) and boundary conforming Delaunay meshes provide good approximation of the geometry of a problem and are able to preserve the essential qualitative properties of the solution for any given resolution in space and time as well as changes in time scales of multiple orders of magnitude. This work provides a brief description of the essential and useful properties of the Voronoi FVM, which look like going more and more out of the mainstream over the last decades, and a motivation why Voronoi FVM deserve to be used more often in practice than they are currently.
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Gärtner, K., Kamenski, L. (2019). Why Do We Need Voronoi Cells and Delaunay Meshes?. In: Garanzha, V., Kamenski, L., Si, H. (eds) Numerical Geometry, Grid Generation and Scientific Computing. Lecture Notes in Computational Science and Engineering, vol 131. Springer, Cham. https://doi.org/10.1007/978-3-030-23436-2_3
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