Abstract
The Moving Finite Element (MFE) method is especially suited to those many highly nonlinear systems which develop shocks and other sharp moving fronts. By allowing the nodes to move and concentrate automatically, and by using an implicit stiff equation solver for the resulting ordinary differential equations (ODEs), we can often solve such problems with far fewer nodes and with far larger time steps than would otherwise be the case. Recently, we have placed special emphasis on development of the gradient weighted MFE method (GWMFE), introduced by Miller in [7] and [8]. Experience with a general purpose one-dimensional code of Carlson and Miller over the past several years (see, for example, [8] and [10]), has shown the method to be extremely efficient and robust. In this paper we report on some preliminary trials with our recently completed two-dimensional GWMFE code which indicate that this superior efficiency and robustness carry over to multidimensions. Our trial examples involve shocks for the system of Burger’s equations in two dimensions and interacting vortices for a complex nonlinear heat equations.
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References
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Carlson, N., Miller, K. (1988). Gradient Weighted Moving Finite Elements in Two Dimensions. In: Dwoyer, D.L., Hussaini, M.Y., Voigt, R.G. (eds) Finite Elements. ICASE/NASA LaRC Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3786-0_7
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DOI: https://doi.org/10.1007/978-1-4612-3786-0_7
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