Adaptive grid generation from harmonic maps on Reimannian manifolds
Journal of Computational Physics
SIAM Journal on Scientific and Statistical Computing
Moving finite elements
Iterative solution methods
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
Moving Mesh Strategy Based on a Gradient Flow Equation for Two-Dimensional Problems
SIAM Journal on Scientific Computing
An r-adaptive finite element method based upon moving mesh PDEs
Journal of Computational Physics
A Study of Monitor Functions for Two-Dimensional Adaptive Mesh Generation
SIAM Journal on Scientific Computing
On the numerical solution of one-dimensional PDEs using adaptive methods based on equidistribution
Journal of Computational Physics
Practical aspects of formulation and solution of moving mesh partial differential equations
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
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
On Resistive MHD Models with Adaptive Moving Meshes
Journal of Scientific Computing
A pseudospectral method of solution of Fisher's equation
Journal of Computational and Applied Mathematics
ELLAM for resolving the kinematics of two-dimensional resistive magnetohydrodynamic flows
Journal of Computational Physics
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
Robust adaptive computation of a one-dimensional Q-tensor model of nematic liquid crystals
Computers & Mathematics with Applications
Hi-index | 31.46 |
Numerical experiments are described which illustrate some important features of the performance of moving mesh methods for solving two-dimensional partial differential equations (PDEs). Here we are concerned with algorithms based on moving mesh methods proposed by W. Huang and R. D. Russell [SIAM J. Sci. Comput. 20, 998 (1999)]. We show that the accuracy of the computations is strongly influenced by the choice of monitor function, and we present a monitor function which yields a higher rate of convergence than those that are commonly used. In an earlier paper [G. Beckett, J. A. Mackenzie, A. Ramage, and D. M. Sloan, J. Comput. Phys. 167, 372 (2001)], we demonstrated a robust and efficient algorithm for problems in one space dimension in which the mesh equation is decoupled from the physical PDE and the time step is controlled automatically. The present work extends this algorithm to deal with problems in two space dimensions.