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Anisotropic interpolation error estimates via orthogonal expansions

100%

Li M., Mao S.

Open Mathematics

2013

tom 11

nr 4

621-629

We prove anisotropic interpolation error estimates for quadrilateral and hexahedral elements with all possible shape function spaces, which cover the intermediate families, tensor product families and serendipity families. Moreover, we show that the anisotropic interpolation error estimates hold for derivatives of any order. This goal is accomplished by investigating an interpolation defined via orthogonal expansions.

Some superconvergence results of high-degree finite element method for a second order elliptic equation with variable coefficients

81%

Guan X., Li M., He W., Jiang Z.

Open Mathematics

2014

tom 12

nr 11

1733-1747

In this paper, some superconvergence results of high-degree finite element method are obtained for solving a second order elliptic equation with variable coefficients on the inner locally symmetric mesh with respect to a point x 0 for triangular meshes. By using of the weak estimates and local symmetric technique, we obtain improved discretization errors of O(h p+1 |ln h|2) and O(h p+2 |ln h|2) when p (≥ 3) is odd and p (≥ 4) is even, respectively. Meanwhile, the results show that the combination of the weak estimates and local symmetric technique is also effective for superconvergence analysis of the second order elliptic equation with variable coefficients.

Ograniczanie wyników

2 Open Mathematics

2 Li M.

1 Guan X.

1 He W.

1 Jiang Z.

1 Mao S.

1 2014

1 2013

Wyniki wyszukiwania

Anisotropic interpolation error estimates via orthogonal expansions

Some superconvergence results of high-degree finite element method for a second order elliptic equation with variable coefficients