Geometric error of finite volume schemes for conservation laws on evolving surfaces

• Published in: Numerische Mathematik Vol. 128; no. 3; pp. 489 - 516
• Main Authors: Giesselmann, Jan, Müller, Thomas
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2014
• Subjects: Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Numerical Analysis; Numerical and Computational Physics; Simulation; Theoretical; 65M08; 58J45; 35L65
• ISSN: 0029-599X; 0945-3245
• DOI: 10.1007/s00211-014-0621-5

This paper studies finite volume schemes for scalar hyperbolic conservation laws on evolving hypersurfaces of R 3 . We compare theoretical schemes assuming knowledge of all geometric quantities to (practical) schemes defined on moving polyhedra approximating the surface. For the former schemes error...