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Abstract:

We prove optimal order error estimates in the H1 norm for the Q1 isoparametric interpolation on convex quadrilateral elements under rather weak hypotheses, improving previously known results. Choose one diagonal and divide the element into two triangles. We show that, if the chosen diagonal is the longest one, then the constant in the error estimate depends only on the maximum angle of the two triangles. Otherwise, the constant depends on that maximum angle and on the ratio between the two diagonals. In particular, we obtain the optimal order error estimate under the maximum angle condition as in the case of triangular elements. Consequently, the error estimate is uniformly valid for a rather general class of degenerate quadrilaterals.

Registro:

Documento: Artículo
Título:Error estimates for Q1 isoparametric elements satisfying a weak angle condition
Autor:Acosta, G.; Durán, R.G.
Filiación:Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Anisotropic elements; Isoparametric finite elements; Lagrange interpolation; Maximum angle condition; Quadrilateral elements
Año:2001
Volumen:38
Número:4
Página de inicio:1073
Página de fin:1088
DOI: http://dx.doi.org/10.1137/S0036142999359104
Título revista:SIAM Journal on Numerical Analysis
Título revista abreviado:SIAM J Numer Anal
ISSN:00361429
CODEN:SJNAA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v38_n4_p1073_Acosta

Referencias:

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Citas:

---------- APA ----------
Acosta, G. & Durán, R.G. (2001) . Error estimates for Q1 isoparametric elements satisfying a weak angle condition. SIAM Journal on Numerical Analysis, 38(4), 1073-1088.
http://dx.doi.org/10.1137/S0036142999359104
---------- CHICAGO ----------
Acosta, G., Durán, R.G. "Error estimates for Q1 isoparametric elements satisfying a weak angle condition" . SIAM Journal on Numerical Analysis 38, no. 4 (2001) : 1073-1088.
http://dx.doi.org/10.1137/S0036142999359104
---------- MLA ----------
Acosta, G., Durán, R.G. "Error estimates for Q1 isoparametric elements satisfying a weak angle condition" . SIAM Journal on Numerical Analysis, vol. 38, no. 4, 2001, pp. 1073-1088.
http://dx.doi.org/10.1137/S0036142999359104
---------- VANCOUVER ----------
Acosta, G., Durán, R.G. Error estimates for Q1 isoparametric elements satisfying a weak angle condition. SIAM J Numer Anal. 2001;38(4):1073-1088.
http://dx.doi.org/10.1137/S0036142999359104