Download BAIL 2010 - Boundary and Interior Layers, Computational and by Rajai S. Alassar (auth.), Carmelo Clavero, José Luis Gracia, PDF

By Rajai S. Alassar (auth.), Carmelo Clavero, José Luis Gracia, Francisco J. Lisbona (eds.)

This quantity will comprise chosen papers from the lectures held on the BAIL 2010 convention, which happened from July fifth to ninth, 2010 in Zaragoza (Spain). The papers current major advances within the modeling, research and building of effective numerical tips on how to remedy boundary and inside layers showing in singular perturbation difficulties. specified emphasis is wear the mathematical foundations of such equipment and their program to actual versions. issues in clinical fields resembling fluid dynamics, quantum mechanics, semiconductor modeling, keep watch over conception, elasticity, chemical reactor conception, and porous media are tested in detail.

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Extra resources for BAIL 2010 - Boundary and Interior Layers, Computational and Asymptotic Methods

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Furthermore, stability and error estimates of order O. H 1 /-norm. ˝// Ä J2 . B. García et al. 2 where R Œ  WD nC1 n N 1 for a sequence b D f gN nD0 . Here, J2 does t nD0 not depend on . From these estimates and by using appropriate changes of variable, analogous estimates in Eulerian coordinates are deduced. t 4 Numerical Results We consider the following example to compare the numerical results obtained with semi-Lagrangian, (full) Lagrangian methods and the PSI method. 001. 1 2 0 cos. 1 if < 0; // if 0 Ä Ä 1; if 1 < ; (10) where D x1 C x2 1=2.

T C h /; (8) b N 1 for a sequence b D f gN where SŒ  WD f nC1 C n gnD0 nD0 . Here, J1 is bounded in the hyperbolic limit. In particular, this result is also valid when D 0. Furthermore, stability and error estimates of order O. H 1 /-norm. ˝// Ä J2 . B. García et al. 2 where R Œ  WD nC1 n N 1 for a sequence b D f gN nD0 . Here, J2 does t nD0 not depend on . From these estimates and by using appropriate changes of variable, analogous estimates in Eulerian coordinates are deduced. t 4 Numerical Results We consider the following example to compare the numerical results obtained with semi-Lagrangian, (full) Lagrangian methods and the PSI method.

For this aim the test functions corresponding to this term are taken from a new space of piecewise constant functions Wh directly related to the flux distribution coefficients ˇiT . xi /ˇiT . h / (see [6] for more details). Notice that it depends on the unknown h due to the non-linear nature of the PSI method. We introduce the number of time steps, N , the time step t D T =N , and the mesh-points, tn D n t for n D 0; 1=2; 1; : : : ; N . Next, we define the form ahn W Vh1 Vh1 ! R for 0 Ä n Ä N as Z ahn .

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