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Full-Text Articles in Physical Sciences and Mathematics
Some Remarks On Interpolation And Best Approximation, Randolph E. Bank, Jeffrey S. Ovall
Some Remarks On Interpolation And Best Approximation, Randolph E. Bank, Jeffrey S. Ovall
Mathematics and Statistics Faculty Publications and Presentations
Sufficient conditions are provided for establishing equivalence between best approximation error and projection/interpolation error in finite-dimensional vector spaces for general (semi)norms. The results are applied to several standard finite element spaces, modes of interpolation and (semi)norms, and a numerical study of the dependence on polynomial degree of constants appearing in our estimates is provided.