The concept of multiresolution-based adaptive DG schemes for non-linear one-dimensional
hyperbolic conservation laws has been developed and investigated analytically and …

This paper constitutes our initial effort in develo** sparse grid discontinuous Galerkin (DG)
methods for high-dimensional partial differential equations (PDEs). Over the past few …

Multiresolution-based mesh adaptivity using biorthogonal wavelets has been quite
successful with finite volume solvers for compressible fluid flow. The extension of the …

Purpose The purpose of this work is to present the implementation of weighted essentially
non-oscillatory (WENO) wavelet methods for solving multiphase flow problems. The …

Adaptive strategies in space and time allow considerable speed-up of finite volume
schemes for conservation laws, while controlling the accuracy of the discretization. In this …

In this paper, we develop an adaptive multiresolution discontinuous Galerkin (DG) scheme
for time-dependent transport equations in multidimensions. The method is constructed using …

Dynamic mesh adaptation methods require suitable refinement indicators. In the absence of
a comprehensive error estimation theory, adaptive mesh refinement (AMR) for nonlinear …

Multiwavelets (MW) enable the compression, analysis and assembly of model data on a
multiresolution grid within Godunov-type solvers based on second-order discontinuous …

A multiresolution analysis (MRA) for solving stochastic conservation laws is proposed. Using
a novel adaptation strategy and a higher-dimensional deterministic problem, a …

In this paper, we develop an adaptive multiresolution discontinuous Galerkin (DG) scheme
for scalar hyperbolic conservation laws in multidimensions. Compared with previous work …