Mimetic finite difference methods

January 8, 2008

Time: January 8, 2008
Lecturer: Dr. rer.nat. Bernd Flemisch, M.Sc.
Lehrstuhl für Hydromechanik und Hydrosystemmodellierung, Institut für Wasserbau, Uni Stuttgart
Venue: Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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Mimetic finite difference methods constitute an alternative frameworkfor the discretization of partial differential equations. The key ideais to discretize the basic operators gradient, curl, and divergence insuch a way that the fundamental mathematical relations of vectorcalculus can be exactly reproduced in the discrete setting. In physicalterms, this corresponds to the most wanted discrete conservation ofmass, energy, etc. In addition, mimetic methods appear most promisingfor managing strong heterogeneities, distorted elements, or hangingnodes. This talk provides an introduction to the methodology,interpretes the resulting numerical model within the frameworks of mixedfinite elements and finite volumes, and illustrates the robustness bymeans of simple numerical examples.
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