An adaptive wavelet viscosity method for hyperbolic conservation laws | Zendy

Castaño Díez Daniel | Zendy; Gunzburger Max | Zendy; Kunoth Angela | Zendy

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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

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