On the multi-level splitting of finite element spaces
Numerische Mathematik
Convergence of spectral methods for nonlinear conservation laws
SIAM Journal on Numerical Analysis
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Wavelets for computer graphics: theory and applications
Wavelets for computer graphics: theory and applications
Adaptive wavelet methods for elliptic operator equations: convergence rates
Mathematics of Computation
Reconstruction of Wavelet Coefficients Using Total Variation Minimization
SIAM Journal on Scientific Computing
Adaptive Wavelet Schemes for Nonlinear Variational Problems
SIAM Journal on Numerical Analysis
A Finite Element, Multiresolution Viscosity Method for Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
Principles of Computational Fluid Dynamics
Principles of Computational Fluid Dynamics
Journal of Computational Physics
Image enhancement and denoising by complex diffusion processes
IEEE Transactions on Pattern Analysis and Machine Intelligence
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For the Burgers equation as an example of a hyperbolic conservation law, we have considered in our previous paper Castano Diez et al. (2008) [8] a weak formulation with a stabilization for handling discontinuities, commonly called a viscosity approach. Numerically, this was realized by locally introducing degrees of freedom around the discontinuities by means of an adaptive wavelet method in an a posteriori fashion. In the present paper, we apply this method to systems of conservation laws, specifically, Euler's equations for gas dynamics. Moreover, as the viscosity stabilization produces some Gibbs phenomena, we discuss different post-processing techniques known from data and image processing together with a number of numerical comparisons.