Optimal Error Estimation for ${\bfH}({\rmcurl})$-Conformingp-Interpolation in Two Dimensions
| Autor: | Norbert Heuer, Alexei Bespalov |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Curl (mathematics)
Numerical Analysis Optimal estimation Applied Mathematics Numerical analysis Mathematical analysis Projection (linear algebra) Finite element method Combinatorics Computational Mathematics symbols.namesake Maxwell's equations symbols Vector field Boundary element method Mathematics |
| Zdroj: | SIAM Journal on Numerical Analysis. 47:3977-3989 |
| ISSN: | 1095-7170 0036-1429 |
| DOI: | 10.1137/090753802 |
| Popis: | In this paper we prove an optimal error estimate for the ${\bf H}({\rm curl})$-conforming projection-based $p$-interpolation operator introduced in [L. Demkowicz and I. Babuska, SIAM J. Numer. Anal., 41 (2003), pp. 1195-1208]. This result is proved on the reference element (either triangle or square) $K$ for regular vector fields in ${\bf H}^r({\rm curl},K)$ with arbitrary $r >0$. The formulation of the result in the ${\bf H}({\rm div})$-conforming setting, which is relevant for the analysis of high-order boundary element approximations for Maxwell's equations, is provided as well. |
| Databáze: | OpenAIRE |
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