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Spectral element methods on unstructured meshes: which interpolation points?

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Spectral element methods on unstructured meshes: which interpolation points?
In the field of spectral element approximations, the interpolation points can be chosen on the basis of different criteria, going from the minimization of the Lebesgue constant to the simplicity of the point generation procedure. In the present paper, we summarize some recent nodal distributions for a high order interpolation in the triangle. We then adopt these points as approximation points for the numerical solution of an elliptic partial differential equation on an unstructured simplicial mesh. The L2 -norm of the approximation error is then analyzed for a model problem. Keywords Spectral elements · Simplicial meshes · Lebesgue constant · High-order interpolation Mathematics Subject Classifications (2010) 65M60 · 65M70 · 41A05
Richard Pasquetti, Francesca Rapetti
Added 29 Jan 2011
Updated 29 Jan 2011
Type Journal
Year 2010
Where NA
Authors Richard Pasquetti, Francesca Rapetti
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