National Science Foundation DMS-1318480 and DMS-1414365.
Finite element method, Vector spaces, Interpolation spaces, Numerical analysis
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.
Bank, R. E., & Ovall, J. S. (2017). Some remarks on interpolation and best approximation. Numerische Mathematik, 1-14.