Abstract
The two numerical methods most frequently used to solve differential equations arising in science and engineering are perhaps the finite difference (FDM) and finite element (FEM) methods. The basic philosophy behind both these methods is to replace the true solution by an approximate one constructed from a suitable set of basis functions. In the case of the FEM the basis functions are usually selected from the set of piecewise continuous polynomials, while the FDM is based on interpolation polynomials [Botha and Pinder (1983)]. This reduces the problem to the simple operation of solving a set of equations
for the expansion coefficients c in the approximating series.
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Botha, J.F., Bakkes, G.N. (1984). Modelling Ground-Water Flow with the Global and Finite Element Methods. In: Laible, J.P., Brebbia, C.A., Gray, W., Pinder, G. (eds) Finite Elements in Water Resources. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11744-6_16
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DOI: https://doi.org/10.1007/978-3-662-11744-6_16
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