Wavelets And Adaptive Grids For The Discontinuous Galerkin Method
Contribuinte(s) |
UNIVERSIDADE DE ESTADUAL DE CAMPINAS |
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Data(s) |
2005
20/01/2016
20/01/2016
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Resumo |
In this paper, space adaptivity is introduced to control the error in the numerical solution of hyperbolic systems of conservation laws. The reference numerical scheme is a new version of the discontinuous Galerkin method, which uses an implicit diffusive term in the direction of the streamlines, for stability purposes. The decision whether to refine or to unrefine the grid in a certain location is taken according to the magnitude of wavelet coefficients, which are indicators of local smoothness of the numerical solution. Numerical solutions of the nonlinear Euler equations illustrate the efficiency of the method. © Springer 2005. 39 1-3 143 154 Abgrall, R., Harten, A., Multiresolution representation in unstructured meshes (1998) SIAM J. Numer. Anal. Bihari, B.L., Harten, A., Multiresolution schemes for the numerical solution of 2-D conservation laws I (1997) SIAM J. Sci. Comput., 18 (2) Bonhaus, D.L., (1998) A Higher Order Accurate Finite Element Method for Viscous Compressible Flows, , Ph.D. thesis, Virginia Polytechnics Institute and State University (November) Brooks, A., Hughes, T., Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations (1982) Comput. Methods Appl. Mech. Engrg., 32 Chiavassa, G., Donat, R., Numerical experiments with multilevel schemes for conservation laws (1999) Godunov's Methods: Theory and Applications, , ed. Toro (Kluwer Academic/Plenum, Dordrecht) Cockburn, B., Shu, C.-W., Runge-Kutta discontinuous Galerkin method for convection-dominated problems (2001) J. Sci. Comput., 16 Cohen, A., Muller, S., Postel, M., Ould-Kabe, S.M., Fully adaptive multiresolution finite volume schemes for conservation laws (2002) Math. Comp., 72 Dahmen, W., Gottschlich-Müller, B., Müller, S., Multiresolution schemes for conservation laws (1998) Numer. Math., 88 Díaz Calle, J.L., Devloo, P.R.B., Gomes, S.M., Stabilized discontinuous Galerkin method for hyperbolic equations Comput. Methods Appl. Mech. Engrg., , to appear Domingues, M.O., Gomes, S.M., Diaz, L.A., Adaptive wavelet representation and differentiation on block-structured grids (2003) Appl. Numer. Math., 8 (3-4) Harten, A., Adaptive multiresolution schemes for shock computations (1994) J. Comput. Phys., 115 Harten, A., Multiresolution representation of data: A general framework (1996) SIAM J. Numer. Anal., 33 Holmström, M., (1997) Wavelet Based Methods for Time Dependent PDE, , Ph.D. thesis, Uppsala University, Sweden Kaibara, M.K., Gomes, S.M., Fully adaptive multiresolution scheme for shock computations (1999) Godunov's Methods: Theory and Applications, , ed. Toro (Kluwer Academic/Plenum, Dordrecht) Sjögreen, B., Numerical experiments with the multiresolution schemes for the compressible Euler equations (1995) J. Comput. Phys., 117 Vasilyev, O.V., Bowman, C., Second generation wavelet collocation method for the solution of partial differential equations (2000) J. Comput. Phys., 165 Waldén, J., Filter bank methods for hyperbolic PDEs (1999) SIAM J. Numer. Anal., 36 |
Identificador |
Numerical Algorithms. , v. 39, n. 1-3, p. 143 - 154, 2005. 10171398 10.1007/s11075-004-3626-9 http://www.repositorio.unicamp.br/handle/REPOSIP/93506 http://repositorio.unicamp.br/jspui/handle/REPOSIP/93506 http://repositorio.unicamp.br/jspui/handle/REPOSIP/203709 2-s2.0-17444415674 |
Idioma(s) |
en |
Relação |
Numerical Algorithms |
Direitos |
fechado |
Fonte |
Scopus |
Tipo |
Artigo de periódico |