An adaptive wavelet viscosity method for hyperbolic conservation laws
Daniel Castaño‐Díez, Max Gunzburger, Angela Kunoth · Numerical Methods for Partial Differential Equations · 2008
Abstract 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