An analysis of time discretization in the finite element solution of hyperbolic problems
Journal of Computational Physics
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Computational algorithms for aerodynamic analysis and design
Applied Numerical Mathematics
Journal of Computational Physics
Flux-corrected transport I. SHASTA, a fluid transport algorithm that works
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
An improved finite-element flux-corrected transport algorithm
Journal of Computational Physics
High-resolution FEM-TVD schemes based on a fully multidimensional flux limiter
Journal of Computational Physics
A Shock-Capturing Algorithm for the Differential Equations of Dilation and Erosion
Journal of Mathematical Imaging and Vision
On the design of general-purpose flux limiters for finite element schemes. I. Scalar convection
Journal of Computational Physics
Explicit and implicit FEM-FCT algorithms with flux linearization
Journal of Computational Physics
FITOVERT: A dynamic numerical model of subsurface vertical flow constructed wetlands
Environmental Modelling & Software
On (essentially) non-oscillatory discretizations of evolutionary convection-diffusion equations
Journal of Computational Physics
Linearity-preserving flux correction and convergence acceleration for constrained Galerkin schemes
Journal of Computational and Applied Mathematics
A flux-corrected transport algorithm for handling the close-packing limit in dense suspensions
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Hi-index | 31.47 |
Flux correction in the finite element context is addressed. Criteria for positivity of the numerical solution are formulated, and the low-order transport operator is constructed from the discrete high-order operator by adding modulated dissipation so as to eliminate negative off-diagonal entries. The corresponding antidiffusive terms can be decomposed into a sum of genuine fluxes (rather than element contributions) which represent bilateral mass exchange between individual nodes. Thereby, essentially one-dimensional flux correction tools can be readily applied to multidimensional problems involving unstructured meshes. The proposed methodology guarantees mass conservation and makes it possible to design both explicit and implicit FCT schemes based on a unified limiting strategy. Numerical results for a number of benchmark problems illustrate the performance of the algorithm.