Approximations of the partial derivatives by averaging

• Autorzy: Josef Dalík
• Języki publikacji: EN

Abstrakty

EN

A straightforward generalization of a classical method of averaging is presented and its essential characteristics are discussed. The method constructs high-order approximations of the l-th partial derivatives of smooth functions u in inner vertices a of conformal simplicial triangulations T of bounded polytopic domains in ℝd for arbitrary d ≥ 2. For any k ≥ l ≥ 1, it uses the interpolants of u in the polynomial Lagrange finite element spaces of degree k on the simplices with vertex a only. The high-order accuracy of the resulting approximations is proved to be a consequence of a certain hypothesis and it is illustrated numerically. The method of averaging studied in [Dalík J., Averaging of directional derivatives in vertices of nonobtuse regular triangulations, Numer. Math., 2010, 116(4), 619–644] provides a solution of this problem in the case d = 2, k = l = 1.

Słowa kluczowe

EN

Regular simplicial triangulation; Lagrange finite element; Averaging the partial derivatives; High-order approximation

Kategorie tematyczne

• 65D25: Numerical differentiation

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 1
• Strony: 44-54

Daty

wydano

2012-02-01

online

2011-12-09

Twórcy

autor

Josef Dalík

• Brno University of Technology

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-011-0107-y