Comparison of Finite-Difference, Finite-Element, and Spectral Methods
In the preceding chapters we have examined the structure and properties of the traditional Galerkin method and observed that its modern developments have gone in two radically different directions. First, finite-element methods use local, low-order polynomial trial functions to generate sparse algebraic equations in terms of meaningful nodal unknowns. Secondly the use of global, orthogonal trial functions permits spectral methods to achieve a high accuracy per degree of freedom.
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