Simple adaptive grids for 1-d initial value problems
Journal of Computational Physics
Computation of sharp phase boundaries by spreading: the planar and spherically symmetric cases
Journal of Computational Physics
Computation of dendrites using a phase field model
Proceedings of the twelfth annual international conference of the Center for Nonlinear Studies on Nonlinearity in Materials Science
ACM Transactions on Mathematical Software (TOMS)
Phase field computations of single-needle crystals, crystal growth, and motion by mean curvature
SIAM Journal on Scientific Computing
Moving mesh partial differential equations (MMPDES) based on the equidistribution principle
SIAM Journal on Numerical Analysis
Computation of three dimensional dendrites with finite elements
Journal of Computational Physics
The phase-field method in the sharp-interface limit: a comparison between model potentials
Journal of Computational Physics
Analysis of Moving Mesh Partial Differential Equations with Spatial Smoothing
SIAM Journal on Numerical Analysis
An explicit, adaptive grid algorithm for one-dimensional initial value problems
Proceedings of international centre for mathematical sciences on Grid adaptation in computational PDES : theory and applications: theory and applications
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
An r-adaptive finite element method based upon moving mesh PDEs
Journal of Computational Physics
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
The numerical solution of one-dimensional phase change problems using an adaptive moving mesh method
Journal of Computational Physics
On the numerical solution of one-dimensional PDEs using adaptive methods based on equidistribution
Journal of Computational Physics
A moving mesh finite element method for the two-dimensional Stefan problems
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Anisotropic mesh adaptation for the solution of the Stefan problem
Journal of Computational Physics
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 comparison of numerical models for one-dimensional Stefan problems
Journal of Computational and Applied Mathematics
Spectral implementation of an adaptive moving mesh method for phase-field equations
Journal of Computational Physics
Journal of Computational Physics
An adaptive mesh redistribution method for the incompressible mixture flows using phase-field model
Journal of Computational Physics
Efficient computation of dendritic growth with r-adaptive finite element methods
Journal of Computational Physics
Consistent Dirichlet boundary conditions for numerical solution of moving boundary problems
Applied Numerical Mathematics
A simple moving mesh method for one- and two-dimensional phase-field equations
Journal of Computational and Applied Mathematics
Hi-index | 31.47 |
A moving mesh method is developed for the numerical solution of one-dimensional phase-change problems modelled by the phase-field equations. The computational mesh is obtained by equidistribution of a monitor function tailored for the functional variation of the phase field in the interfacial region. Existence and uniqueness of the discretised equations using a moving mesh are also established. Numerical results are given for classical and modified Stefan test problems. The numerical algorithm is relatively simple and is shown to be far more efficient than fixed grid methods.