SIAM Journal on Scientific and Statistical Computing
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
A high dimensional moving mesh strategy
Proceedings of international centre for mathematical sciences on Grid adaptation in computational PDES : theory and applications: theory and applications
Design and Application of a Gradient-Weighted Moving Finite Element Code II: in Two Dimensions
SIAM Journal on Scientific Computing
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
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
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)
Moving mesh methods with locally varying time steps
Journal of Computational Physics
On Resistive MHD Models with Adaptive Moving Meshes
Journal of Scientific Computing
A fully adaptive reaction-diffusion integration scheme with applications to systems biology
Journal of Computational Physics
Journal of Scientific Computing
Dimension-splitting data points redistribution for meshless approximation
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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In this paper we describe an adaptive moving mesh technique and its application to reaction-diffusion models from chemistry. 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 is 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 PDEs and the adaptive PDEs are decoupled. Further, to avoid solving large nonlinear systems, a second-order implicit-explicit time-integration method in combination with the iterative method Bi-CGSTAB is applied in the method-of-lines procedure. Numerical examples are given in one and two space dimensions.