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Registro 1 de 2, Base de información BIBCYT |
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Información de existencia
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Palabras Claves:
ELLIPTIC PROBLEMS,
NONCONFORMING FINITE ELEMENTS,
QUADRILATERAL |
Resumen
A P1-nonconforming quadrilateral finite element is introduced for second-order elliptic problems in two dimensions. Unlike the usual quadrilateral nonconforming finite elements, which contain quadratic polynomials or polynomials of degree greater than 2, our element consists of only piecewise linear polynomials that are continuous at the midpoints of edges. One of the benefits of using our element is convenience in using rectangular or quadrilateral meshes with the least degrees of freedom among the nonconforming quadrilateral elements. An optimal rate of convergence is obtained. Also a nonparametric reference scheme is introduced in order to systematically compute stiffness and mass matrices on each quadrilateral. An extension of the P1-nonconforming element to three dimensions is also given. Finally, several numerical results are reported to confirm the effective nature of the proposed new element. |
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Registro 2 de 2, Base de información BIBCYT |
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Información de existencia
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Palabras Claves:
CONVECTION-DIFFUSION PROBLEMS,
ERROR ESTIMATES,
NONCONFORMING FINITE ELEMENTS,
STREAMLINE DIFFUSION METHOD |
Resumen
We consider a nonconforming streamline diffusion finite element method for solving convection-diffusion problems. The loss of the Galerkin orthogonality of the streamline diffusion method when applied to nonconforming finite element approximations results in an additional error term which cannot be estimated uniformly with respect to the perturbation parameter for the standard piecewise linear or rotated bilinear elements. Therefore, starting from the Crouzeix--Raviart element, we construct a modified nonconforming first order finite element space on shape regular triangular meshes satisfying a patch test of higher order. A rigorous error analysis of this P1mod element applied to a streamline diffusion discretization is given. The numerical tests show the robustness and the high accuracy of the new method. |