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A Moving Collocation Method for Solving Time Dependent Partial Differential Equations (1995)
| Venue: | Appl. Numer. Math |
| Citations: | 17 - 3 self |
BibTeX
@ARTICLE{Huang95amoving,
author = {Weizhang Huang and Robert D. Russell},
title = {A Moving Collocation Method for Solving Time Dependent Partial Differential Equations},
journal = {Appl. Numer. Math},
year = {1995},
volume = {20},
pages = {101--116}
}
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Abstract
A new moving mesh method is introduced for solving time dependent partial differential equations (PDEs) in divergence form. The method uses a cell-averaging cubic Hermite collocation discretization for the physical PDEs and a three point finite difference discretization for the PDE which determines the moving mesh. Numerical results are presented for a selection of difficult bench-mark problems, including Burgers' equation and Sod's shocktube problem. They indicate third order convergence for the method, slower than the traditional (fourth order) cubic Hermite collocation on a fixed mesh but much faster than the first order of the commonly used moving finite difference methods. Numerical experiments also show that, in comparison with finite differences and fixed mesh collocation, moving collocation produces more accurate results for small and moderate numbers of mesh points. 1 Introduction A variety of adaptive mesh methods have been widely used of late to solve time dependent partial ...
Keyphrases
time dependent partial differential equation moving collocation method adaptive mesh method introduction variety divergence form cell-averaging cubic hermite collocation discretization physical pdes accurate result time dependent partial shocktube problem finite difference third order convergence fourth order moderate number mesh point numerical result finite difference method numerical experiment mesh method hermite collocation point finite difference discretization fixed mesh first order difficult bench-mark problem mesh collocation
