Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Computational solution of two-dimensional unsteady PDEs using moving mesh methods
Journal of Computational Physics
Moving mesh finite element methods based on harmonic maps
Scientific computing and applications
Applied Numerical Mathematics
Approaches for generating moving adaptive meshes: location versus velocity
Applied Numerical Mathematics - Special issue: 2nd international workshop on numerical linear algebra, numerical methods for partial differential equations and optimization
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
A three-dimensional adaptive method based on the iterative grid redistribution
Journal of Computational Physics
On Resistive MHD Models with Adaptive Moving Meshes
Journal of Scientific Computing
Adaptive unstructured volume remeshing - I: The method
Journal of Computational Physics
Space---Time Adaptive Solution of First Order PDES
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
A splitting moving mesh method for reaction-diffusion equations of quenching type
Journal of Computational Physics
Journal of Computational Physics
Spectral implementation of an adaptive moving mesh method for phase-field equations
Journal of Computational Physics
An adaptive mesh redistribution method for the incompressible mixture flows using phase-field model
Journal of Computational Physics
ELLAM for resolving the kinematics of two-dimensional resistive magnetohydrodynamic flows
Journal of Computational Physics
Adaptive pseudospectral solution of a diffuse interface model
Journal of Computational and Applied Mathematics
Exponential splitting time integration for pseudospectral methods on moving meshes
Journal of Computational and Applied Mathematics
A simple moving mesh method for one- and two-dimensional phase-field equations
Journal of Computational and Applied Mathematics
Adaptive mesh redistribution method for domains with complex boundaries
Journal of Computational Physics
Optimal mass transport for higher dimensional adaptive grid generation
Journal of Computational Physics
Moving mesh method for problems with blow-up on unbounded domains
Numerical Algorithms
Journal of Computational Physics
Journal of Computational and Applied Mathematics
A moving mesh generation strategy for solving an injector internal flow problem
Mathematical and Computer Modelling: An International Journal
Hi-index | 0.06 |
In this paper we introduce a moving mesh method for solving PDEs in two dimensions. It can be viewed as a higher-dimensional generalization of the moving mesh PDE (MMPDE) strategy developed in our previous work for one-dimensional problems [W. Huang, Y. Ren, and R. D. Russell, SIAM J. Numer. Anal., 31 (1994), pp. 709--730]. The MMPDE is derived from a gradient flow equation which arises using a mesh adaptation functional in turn motivated from the theory of harmonic maps. Geometrical interpretations are given for the gradient equation and functional, and basic properties of this MMPDE are discussed. Numerical examples are presented where the method is used both for mesh generation and for solving time-dependent PDEs. The results demonstrate the potential of the mesh movement strategy to concentrate the mesh points so as to adapt to special problem features and to also preserve a suitable level of mesh orthogonality.