Lagrange and average interpolation over 3D anisotropic elements
An average interpolation is introduced for 3-rectangles and tetrahedra, and optimal order error estimates in the H1 norm are proved. The constant in the estimate depends "weakly" (improving the results given in Durán (Math. Comp. 68 (1999) 187-199) on the uniformity of the mesh in each dir...
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todo:paper_03770427_v135_n1_p91_Acosta2023-10-03T15:31:28Z Lagrange and average interpolation over 3D anisotropic elements Acosta, G. Anisotropic elements Average interpolation Lagrange interpolation Maximum angle condition Angle measurement Anisotropy Error analysis Estimation Lagrange interpolation Interpolation mathematical method An average interpolation is introduced for 3-rectangles and tetrahedra, and optimal order error estimates in the H1 norm are proved. The constant in the estimate depends "weakly" (improving the results given in Durán (Math. Comp. 68 (1999) 187-199) on the uniformity of the mesh in each direction. For tetrahedra, the constant also depends on the maximum angle of the element. On the other hand, merging several known results (Acosta and Durán, SIAM J. Numer. Anal. 37 (1999) 18-36; Durán, Math. Comp. 68 (1999) 187-199; Krizek, SIAM J. Numer. Anal. 29 (1992) 513-520; A1 Shenk, Math. Comp. 63 (1994) 105-119), we prove optimal order error for the P1-Lagrange interpolation in W1,p, > 2, with a constant depending on p as well as the maximum angle of the element. Again, under the maximum angle condition, optimal order error estimates are obtained in the H1 norm for higher degree interpolations. © 2001 Elsevier Science B.V. All rights reserved. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03770427_v135_n1_p91_Acosta |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Anisotropic elements Average interpolation Lagrange interpolation Maximum angle condition Angle measurement Anisotropy Error analysis Estimation Lagrange interpolation Interpolation mathematical method |
| spellingShingle |
Anisotropic elements Average interpolation Lagrange interpolation Maximum angle condition Angle measurement Anisotropy Error analysis Estimation Lagrange interpolation Interpolation mathematical method Acosta, G. Lagrange and average interpolation over 3D anisotropic elements |
| topic_facet |
Anisotropic elements Average interpolation Lagrange interpolation Maximum angle condition Angle measurement Anisotropy Error analysis Estimation Lagrange interpolation Interpolation mathematical method |
| description |
An average interpolation is introduced for 3-rectangles and tetrahedra, and optimal order error estimates in the H1 norm are proved. The constant in the estimate depends "weakly" (improving the results given in Durán (Math. Comp. 68 (1999) 187-199) on the uniformity of the mesh in each direction. For tetrahedra, the constant also depends on the maximum angle of the element. On the other hand, merging several known results (Acosta and Durán, SIAM J. Numer. Anal. 37 (1999) 18-36; Durán, Math. Comp. 68 (1999) 187-199; Krizek, SIAM J. Numer. Anal. 29 (1992) 513-520; A1 Shenk, Math. Comp. 63 (1994) 105-119), we prove optimal order error for the P1-Lagrange interpolation in W1,p, > 2, with a constant depending on p as well as the maximum angle of the element. Again, under the maximum angle condition, optimal order error estimates are obtained in the H1 norm for higher degree interpolations. © 2001 Elsevier Science B.V. All rights reserved. |
| format |
JOUR |
| author |
Acosta, G. |
| author_facet |
Acosta, G. |
| author_sort |
Acosta, G. |
| title |
Lagrange and average interpolation over 3D anisotropic elements |
| title_short |
Lagrange and average interpolation over 3D anisotropic elements |
| title_full |
Lagrange and average interpolation over 3D anisotropic elements |
| title_fullStr |
Lagrange and average interpolation over 3D anisotropic elements |
| title_full_unstemmed |
Lagrange and average interpolation over 3D anisotropic elements |
| title_sort |
lagrange and average interpolation over 3d anisotropic elements |
| url |
http://hdl.handle.net/20.500.12110/paper_03770427_v135_n1_p91_Acosta |
| work_keys_str_mv |
AT acostag lagrangeandaverageinterpolationover3danisotropicelements |
| _version_ |
1807322943119687680 |