SIAM Journal on Scientific and Statistical Computing
Local uniform grid refinement and systems of coupled partial differential equations
Applied Numerical Mathematics
An adaptive grid with directional control
Journal of Computational Physics
Implicit-explicit methods for time-dependent partial differential equations
SIAM Journal on Numerical Analysis
An Adaptive Grid Method and Its Application to Steady Euler Flow Calculations
SIAM Journal on Scientific Computing
Moving Mesh Strategy Based on a Gradient Flow Equation for Two-Dimensional Problems
SIAM Journal on Scientific Computing
On the numerical solution of one-dimensional PDEs using adaptive methods based on equidistribution
Journal of Computational Physics
Computational solution of two-dimensional unsteady PDEs using moving mesh methods
Journal of Computational Physics
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
Variational mesh adaptation II: error estimates and monitor functions
Journal of Computational Physics
Tensor-product adaptive grids based on coordinate transformations
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on boundary and interior layers - computational and asymptotic methods (BAIL 2002)
Adaptive moving mesh computations for reaction--diffusion systems
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the 2nd international conference on advanced computational methods in engineering (ACOMEN2002) Liege University, Belgium, 27-31 May 2002
Moving Mesh Discontinuous Galerkin Method for Hyperbolic Conservation Laws
Journal of Scientific Computing
A simple moving mesh method for one-and two-dimensional phase-field equations
Journal of Computational and Applied Mathematics - Special issue: International conference on mathematics and its application
An efficient adaptive mesh redistribution method for a non-linear Dirac equation
Journal of Computational Physics
Level Set Calculations for Incompressible Two-Phase Flows on a Dynamically Adaptive Grid
Journal of Scientific Computing
Resolving the shock-induced combustion by an adaptive mesh redistribution method
Journal of Computational Physics
ELLAM for resolving the kinematics of two-dimensional resistive magnetohydrodynamic flows
Journal of Computational Physics
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
A simple moving mesh method for one- and two-dimensional phase-field equations
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Dimension-splitting data points redistribution for meshless approximation
Journal of Computational and Applied Mathematics
Simulating finger phenomena in porous media with a moving finite element method
Journal of Computational Physics
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In this paper we describe an adaptive moving mesh technique and its application to convection-diffusion models from magnetohydrodynamics (MHD). The method is based on a coordinate transformation between physical and computational coordinates. The transformation can be viewed as a solution of adaptive mesh partial differential equations (PDEs) which are derived from the minimization of a mesh-energy integral. For an efficient implementation we have used an approach in which the numerical solution of the physical PDE model and the adaptive PDEs are decoupled. Further, to avoid solving large nonlinear systems, an implicit-explicit method is applied for the time integration in combination with the iterative method Bi-CGSTAB. The adaptive mesh can be viewed as a 2D variant of the equidistribution principle, and it has the ability to track individual features of the physical solutions in the developing plasma flows. The results of a series of numerical experiments are presented which cover several aspects typifying resistive magnetofluid-dynamics.