An analysis of accuracy of finite difference and finite element methods for the wave equation Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/tm70mx994

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  • In this paper, Fourier analysis is used to investigate various approximation methods for the one- and two-dimensional wave equations. The spatial derivatives are approximated by the second order centered finite difference method, the linear and quadratic finite element methods, and the fourth order centered finite difference method. The approximation schemes thus obtained shall be continuous in time. Using Fourier analysis, their general solutions can be obtained. Group velocities of these solutions are then compared to the group velocity of the solution to the wave equation. These comparisons will yield a measure of accuracy for the approximation schemes. Finally, we obtain numerical computing schemes by using the second order centered finite difference method in time. Group velocities for these fully discrete schemes are also analyzed and the Courant number for each computing scheme will be shown to have an effect on its accuracy. In the one- and two-dimensional case, numerical results are given to back up the analysis.
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