Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
Iterative Procedures for Nonlinear Integral Equations
Journal of the ACM (JACM)
Flux correction tools for finite elements
Journal of Computational Physics
Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
MooNMD – a program package based on mapped finite element methods
Computing and Visualization in Science
SIAM Journal on Scientific Computing
Adaptive multiresolution WENO schemes for multi-species kinematic flow models
Journal of Computational Physics
A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids
Journal of Computational Physics
Adaptive Time-Stepping for Incompressible Flow Part I: Scalar Advection-Diffusion
SIAM Journal on Scientific Computing
Explicit and implicit FEM-FCT algorithms with flux linearization
Journal of Computational Physics
ENO adaptive method for solving one-dimensional conservation laws
Applied Numerical Mathematics
SIAM Journal on Numerical Analysis
Anderson Acceleration for Fixed-Point Iterations
SIAM Journal on Numerical Analysis
Hi-index | 31.45 |
Finite element and finite difference discretizations for evolutionary convection-diffusion-reaction equations in two and three dimensions are studied which give solutions without or with small under- and overshoots. The studied methods include a linear and a nonlinear FEM-FCT scheme, simple upwinding, an ENO scheme of order 3, and a fifth order WENO scheme. Both finite element methods are combined with the Crank-Nicolson scheme and the finite difference discretizations are coupled with explicit total variation diminishing Runge-Kutta methods. An assessment of the methods with respect to accuracy, size of under- and overshoots, and efficiency is presented, in the situation of a domain which is a tensor product of intervals and of uniform grids in time and space. Some comments to the aspects of adaptivity and more complicated domains are given. The obtained results lead to recommendations concerning the use of the methods.