A moving mesh numerical method for hyperbolic conservation laws
Mathematics of Computation
Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Ten lectures on wavelets
Triangle based adaptive stencils for the solution of hyperbolic conservation laws
Journal of Computational Physics
An error estimate for finite volume methods for multidimensional conservation laws
Mathematics of Computation
Adaptive multiresolution schemes for shock computations
Journal of Computational Physics
Numerical experiments with the multiresolution scheme for the compressible Euler equations
Journal of Computational Physics
Multiresolution Schemes for the Numerical Solution of 2-D Conservation Laws I
SIAM Journal on Scientific Computing
Multiresolution schemes on triangles for scalar conservation laws
Journal of Computational Physics
Adaptive wavelet methods for elliptic operator equations: convergence rates
Mathematics of Computation
Stationary Subdivision
A conservative fully adaptive multiresolution algorithm for parabolic PDEs
Journal of Computational Physics
Adaptive biorthogonal spline schemes for advection-reaction equations
Journal of Computational Physics
An adaptive multiscale finite volume solver for unsteady and steady state flow computations
Journal of Computational Physics
Fully Adaptive Multiscale Schemes for Conservation Laws Employing Locally Varying Time Stepping
Journal of Scientific Computing
High order Hybrid central-WENO finite difference scheme for conservation laws
Journal of Computational and Applied Mathematics
Adaptive multiresolution WENO schemes for multi-species kinematic flow models
Journal of Computational Physics
A multiresolution finite volume scheme for two-dimensional hyperbolic conservation laws
Journal of Computational and Applied Mathematics
An adaptive multiresolution scheme with local time stepping for evolutionary PDEs
Journal of Computational Physics
A wavelet-MRA-based adaptive semi-Lagrangian method for the relativistic Vlasov-Maxwell system
Journal of Computational Physics
Multiscale cell-based coarsening for discontinuous problems
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
Finite volume multischeme for hyperbolic conservation laws
FANDB'09 Proceedings of the 2nd WSEAS international conference on Finite differences, finite elements, finite volumes, boundary elements
A Direct and Accurate Adaptive Semi-Lagrangian Scheme for the Vlasov-Poisson Equation
International Journal of Applied Mathematics and Computer Science - Scientific Computation for Fluid Mechanics and Hyperbolic Systems
Adaptive Multiresolution Methods for the Simulation of Waves in Excitable Media
Journal of Scientific Computing
Grid structure impact in sparse point representation of derivatives
Journal of Computational and Applied Mathematics
Adaptive Timestep Control for Nonstationary Solutions of the Euler Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
Applied Numerical Mathematics
An adaptive multiresolution method on dyadic grids: Application to transport equations
Journal of Computational and Applied Mathematics
A semi-Lagrangian AMR scheme for 2D transport problems in conservation form
Journal of Computational Physics
A one-time truncate and encode multiresolution stochastic framework
Journal of Computational Physics
Well-Balanced Adaptive Mesh Refinement for shallow water flows
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 0.06 |
The use of multiresolution decompositions in the context of finite volume schemes for conservation laws was first proposed by A. Harten for the purpose of accelerating the evaluation of numerical fluxes through an adaptive computation. In this approach the solution is still represented at each time step on the finest grid, resulting in an inherent limitation of the potential gain in memory space and computational time. The present paper is concerned with the development and the numerical analysis of fully adaptive multiresolution schemes, in which the solution is represented and computed in a dynamically evolved adaptive grid. A crucial problem is then the accurate computation of the flux without the full knowledge of fine grid cell averages. Several solutions to this problem are proposed, analyzed, and compared in terms of accuracy and complexity.