Article ID Journal Published Year Pages File Type
10356460 Journal of Computational Physics 2005 25 Pages PDF
Abstract
In this paper, we first describe a fourth order accurate finite difference discretization for both the Laplace equation and the heat equation with Dirichlet boundary conditions on irregular domains. In the case of the heat equation we use an implicit discretization in time to avoid the stringent time step restrictions associated with requirements for explicit schemes. We then turn our focus to the Stefan problem and construct a third order accurate method that also includes an implicit time discretization. Multidimensional computational results are presented to demonstrate the order accuracy of these numerical methods.
Related Topics
Physical Sciences and Engineering Computer Science Computer Science Applications
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