Uniformly high-order accurate nonoscillatory schemes
SIAM Journal on Numerical Analysis
Evolution-Galerkin methods and their supraconvergence
Numerische Mathematik
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
A synchronous and iterative flux-correction formalism for coupled transport equations
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Convergence Analysis for a Class of High-Order Semi-Lagrangian Advection Schemes
SIAM Journal on Numerical Analysis
Multidimensional upwinding. Part I. The method of transport for solving the Euler equations
Journal of Computational Physics
Multidimensional upwinding. Part II. Decomposition of the Euler equations into advection equations
Journal of Computational Physics
On the Analysis of Finite Volume Methods for Evolutionary Problems
SIAM Journal on Numerical Analysis
Incremental remapping as a transport&slash;advection algorithm
Journal of Computational Physics
Lagrange—Galerkin methods on spherical geodesic grids: the shallow water equations
Journal of Computational Physics
A summary of numerical methods for time-dependent advection-dominated partial differential equations
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Flux-based methods of characteristics for coupled transport equations in porous media
Computing and Visualization in Science
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Stability of Some Generalized Godunov Schemes With Linear High-Order Reconstructions
Journal of Scientific Computing
Hi-index | 31.47 |
A new, conservative semi-Lagrangian formulation is proposed for the discretization of the scalar advection equation in flux form. The approach combines the accuracy and conservation properties of the Discontinuous Galerkin (DG) method with the computational efficiency and robustness of Semi-Lagrangian (SL) techniques. Unconditional stability in the von Neumann sense is proved for the proposed discretization in the one-dimensional case. A monotonization technique is then introduced, based on the Flux Corrected Transport approach. This yields a multi-dimensional monotonic scheme for the piecewise constant component of the computed solution that is characterized by a smaller amount of numerical diffusion than standard DG methods. The accuracy and stability of the method are further demonstrated by two-dimensional tracer advection tests in the case of incompressible flows. The comparison with results obtained by standard SL and DG methods highlights several advantages of the new technique.