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Volume 3, Issue 2
Mesh Sensitivity for Numerical Solutions of Phase-Field Equations Using r-Adaptive Finite Element Methods

Heyu Wang & Ruo Li

Commun. Comput. Phys., 3 (2008), pp. 357-375.

Published online: 2008-03

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  • Abstract

There have been several recent papers on developing moving mesh methods for solving phase-field equations. However, it is observed that some of these moving mesh solutions are essentially different from the solutions on very fine fixed meshes. One of the purposes of this paper is to understand the reason for the differences. We carried out numerical sensitivity studies systematically in this paper and it can be concluded that for the phase-field equations, the numerical solutions are very sensitive to the starting mesh and the monitor function. As a separate issue, an efficient alternating Crank-Nicolson time discretization scheme is developed for solving the nonlinear system resulting from a finite element approximation to the phase-field equations.

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@Article{CiCP-3-357, author = {Heyu Wang and Ruo Li }, title = {Mesh Sensitivity for Numerical Solutions of Phase-Field Equations Using r-Adaptive Finite Element Methods}, journal = {Communications in Computational Physics}, year = {2008}, volume = {3}, number = {2}, pages = {357--375}, abstract = {

There have been several recent papers on developing moving mesh methods for solving phase-field equations. However, it is observed that some of these moving mesh solutions are essentially different from the solutions on very fine fixed meshes. One of the purposes of this paper is to understand the reason for the differences. We carried out numerical sensitivity studies systematically in this paper and it can be concluded that for the phase-field equations, the numerical solutions are very sensitive to the starting mesh and the monitor function. As a separate issue, an efficient alternating Crank-Nicolson time discretization scheme is developed for solving the nonlinear system resulting from a finite element approximation to the phase-field equations.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7858.html} }
TY - JOUR T1 - Mesh Sensitivity for Numerical Solutions of Phase-Field Equations Using r-Adaptive Finite Element Methods AU - Heyu Wang & Ruo Li JO - Communications in Computational Physics VL - 2 SP - 357 EP - 375 PY - 2008 DA - 2008/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7858.html KW - AB -

There have been several recent papers on developing moving mesh methods for solving phase-field equations. However, it is observed that some of these moving mesh solutions are essentially different from the solutions on very fine fixed meshes. One of the purposes of this paper is to understand the reason for the differences. We carried out numerical sensitivity studies systematically in this paper and it can be concluded that for the phase-field equations, the numerical solutions are very sensitive to the starting mesh and the monitor function. As a separate issue, an efficient alternating Crank-Nicolson time discretization scheme is developed for solving the nonlinear system resulting from a finite element approximation to the phase-field equations.

Heyu Wang and Ruo Li . (2008). Mesh Sensitivity for Numerical Solutions of Phase-Field Equations Using r-Adaptive Finite Element Methods. Communications in Computational Physics. 3 (2). 357-375. doi:
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