Data di Pubblicazione:
2015
Citazione:
Approximating Gradients with Continuous Piecewise Polynomial Functions / A. Veeser. - In: FOUNDATIONS OF COMPUTATIONAL MATHEMATICS. - ISSN 1615-3375. - (2015). [Epub ahead of print] [10.1007/s10208-015-9262-z]
Abstract:
Motivated by conforming finite element methods for elliptic problems of second order, we analyze the approximation of the gradient of a target function by continuous piecewise polynomial functions over a simplicial mesh. The main result is that the global best approximation error is equivalent to an appropriate sum in terms of the local best approximation errors on elements. Thus, requiring continuity does not downgrade local approximation capability and discontinuous piecewise polynomials essentially do not offer additional approximation power, even for a fixed mesh. This result implies error bounds in terms of piecewise regularity over the whole admissible smoothness range. Moreover, it allows for simple local error functionals in adaptive tree approximation of gradients.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
A priori error estimates; Adaptive tree approximation; Approximation of gradients; Continuous piecewise polynomials; Discontinuous elements; Finite elements; Lagrange elements; Analysis; Applied Mathematics; Computational Mathematics; Computational Theory and Mathematics
Elenco autori:
A. Veeser
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