By Peter D. Lax (auth.), Carlos A. de Moura, Carlos S. Kubrusly (eds.)

ISBN-10: 0817683933

ISBN-13: 9780817683931

ISBN-10: 0817683941

ISBN-13: 9780817683948

This quantity includes a gently chosen choice of articles rising from and pertinent to the 2010 CFL-80 convention in Rio de Janeiro, celebrating the 80th anniversary of the Courant-Friedrichs-Lewy (CFL) . a massive bring about the sphere of numerical research, the CFL has inspired the examine of many vital mathematicians during the last 8 a long time, and this paintings is intended to take inventory of its most crucial and present applications.

The Courant–Friedrichs–Lewy (CFL) situation: eighty Years After its Discovery will be of curiosity to training mathematicians, engineers, physicists, and graduate scholars who paintings with numerical methods.

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Extra resources for The Courant–Friedrichs–Lewy (CFL) Condition: 80 Years After Its Discovery

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That collection of possible questions and answers (not necessarily explicit) becomes the means of accepting or rejecting proposed new members. If two or three mathematicians do more than merely communicate about some mathematical topic, but actually collaborate to dig up new information and understanding about it, then the matching of their mental models must be even closer. 26 R. Hersh They may need to establish a congruence between their subconscious thinking about it as well as their conscious thinking.

The spatial discretization is based on DG methods. Note that it is enough to consider DG methods for the scalar advection–diffusion equation, ∂u + ∂t 1≤i≤n ∂ fi (u) − ∂xi aij i≤j ≤n ∂ u = 0, ∂xj (4) as we can apply similar spatial discretization to each component of (1a)–(1e). In (4), fi is convection flux, aij are diffusion coefficients with the condition that the matrix (aij )ij is symmetric and semi-positive definite, so there exists a symmetric matrix (bij ) such that aij = bil blj . 1 Variational Formulation Following [10], we introduce an auxiliary variable ql = (4) as ∂u + ∂t 1≤i≤n ql − 1≤j ≤n where glj = u 0 blj ∂ fi (u) − ∂xi ∂glj = 0, ∂xj ∂u 1≤j ≤n blj ∂xj and rewrite bil ql = 0, (5a) i≤l≤n for l = 1, .

It was proved in [17] that the coefficients of the basis functions for a solution decay exponentially with polynomial order, thus the numerical solution converges exponentially as the maximum polynomial order of the approximation is increased. 3 Time Stepping To advance solutions in time, the RKDG method uses a Runge–Kutta (RK) time marching scheme. Here we present the second-, third-, and fourth-order accurate RKDG schemes. For second- and third-order simulations, we present the TVD RK schemes of Shu (see [18]).

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The Courant–Friedrichs–Lewy (CFL) Condition: 80 Years After Its Discovery by Peter D. Lax (auth.), Carlos A. de Moura, Carlos S. Kubrusly (eds.)


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