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An adaptive wavelet viscosity method for hyperbolic conservation laws
Author(s) -
Castaño Díez Daniel,
Gunzburger Max,
Kunoth Angela
Publication year - 2008
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20322
Subject(s) - mathematics , conservation law , classification of discontinuities , wavelet , finite element method , partial differential equation , partial derivative , spline (mechanical) , nonlinear system , mathematical analysis , computer science , quantum mechanics , artificial intelligence , engineering , thermodynamics , physics , structural engineering
We extend the multiscale finite element viscosity method for hyperbolic conservation laws developed in terms of hierarchical finite element bases to a (pre‐orthogonal spline‐)wavelet basis. Depending on an appropriate error criterion, the multiscale framework allows for a controlled adaptive resolution of discontinuities of the solution. The nonlinearity in the weak form is treated by solving a least‐squares data fitting problem. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008