Discontinuous Galerkin Methods: Theory, Compuration and by Bernardo Cockburn, George E. Karniadakis, Chi-Wang Shu

By Bernardo Cockburn, George E. Karniadakis, Chi-Wang Shu

This quantity comprises present growth of a brand new category of finite point process, the Discontinuous Galerkin approach (DGM), which has been less than quick advancements lately and has came across its use in a short time in such diversified purposes as aeroacoustics, semi-conductor gadget simulation, turbomachinery, turbulent flows, fabrics processing, Magneto-hydro-dynamics, plasma simulations and picture processing. whereas there was loads of curiosity in DGM from mathematicians, physicists and engineers, merely scattered info is accessible and there was no past attempt in organizing and publishing the prevailing quantity of data in this topic. the present quantity organizes this information and it covers either theoretical in addition to sensible problems with the Discontinuous Galerkin strategy.

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128) 2 oC ~ oA' oC' i=l • Hierin ist die Ableitung OW / Ai nach Vorgabe von wals Funktion der Hauptdehnungen, s. B. (OGDEN 1984), S. 482 ff, direkt bestimmbar. 129) OC = 2 Ai Ni&; Ni. Damit erhalten wir für die 2. 130) 48 3. Kontinuumsmechanische Grundgleichungen In dieser Gleichung wird nicht im Sinne der EINSTEINsehen Summenkonvention über i summiert, was durch die Klammer am Index zu Ausdruck gebracht wird. 23) des rechten CAUCHYGREENschen Verzerrungsmaßes zeigt, daß Sund C die gleichen Eigenvektoren besitzen, was mit der Beschränkung auf isotropes Materialverhalten konsistent ist.

B. (OGDEN 1984), S. 11) gegeben. In dieser Gleichung ist n der Flächennormalenvektor in cp(B) und N der Flächennormalenvektor in B, s. 2. 2. Transformation differentieller Größen J ist die in GI. 8) definierte JAcoBldeterminante, und da bzw. dA sind Flächenelemente in der jeweiligen Konfiguration. Für die 'Iransformation der Volumenelemente von der Ausgangs- in die Momentankonfiguration gilt dv = JdV. 14) der Verschiebungsgradient definiert ist. 2 Verzerrungsmaße In diesem Abschnitt werden unterschiedliche Verzerrungsmaße diskutiert, die bei späteren Aufgabenstellungen Verwendung finden werden.

B. (LUBLINER 1990), S. 453 ff). Natürlich sollten auch die Auswirkungen der Formulierung auf die numerischen Methoden berücksichtigt werden, da hier erhebliche Unterschiede in der Effizienz auftreten können. Aus diesem Grund werden im folgenden die Verzerrungsmaße und auch die weiteren Gleichungen sowohl mit Bezug auf die Referenzkonfiguration B als auch mit Bezug auf die Momentankonfiguration tp(B) angegeben. R. große Buchstaben Tensoren, die auf B bezogen sind; während Tensoren, die in der Momentankonfiguration tp(B) wirken, durch kleine Buchstaben beschrieben werden.

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