From continuous recovery to discrete filtering in numerical approximations of conservation laws Original Research Article

Modern numerical approximations of conservation laws rely on numerical dissipation as a means of stabilization. The older, alternative approach is the use of central differencing with a dose of artificial dissipation. In this paper we review the successful class of weighted essentially non-oscillatory finite volume schemes which comprise sophisticated methods of the first kind. New developments in image processing have made new devices possible which can serve as highly nonlinear artificial dissipation terms. We view artificial dissipation as discrete filter operation and introduce several new algorithms inspired by image processing.