Stabilization of low-order cross-grid PkQl mixed finite elements
In this paper we analyze a low-order family of mixed finite element methods for the numerical solution of the Stokes problem and a second order elliptic problem, in two space dimensions. In these schemes, the pressure is interpolated on a mesh of rectangular elements, while the velocity is approxima...
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| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
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Elsevier B.V.
2018
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| LEADER | 09283caa a22008777a 4500 | ||
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| 001 | PAPER-17075 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518204812.0 | ||
| 008 | 190410s2018 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-85029857503 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Armentano, M.G. | |
| 245 | 1 | 0 | |a Stabilization of low-order cross-grid PkQl mixed finite elements |
| 260 | |b Elsevier B.V. |c 2018 | ||
| 506 | |2 openaire |e Política editorial | ||
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| 504 | |a Brezzi, F., Falk, R., Stability of higher-order Hood-Taylor methods (1991) SIAM J. Numer. Anal., 28 (3), pp. 581-590 | ||
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| 504 | |a Bochev, P.B., Dohrmann, C.R., Gunzburger, M.D., Stabilization of low-order mixed finite elements for the Stokes equations (2006) SIAM J. Numer. Anal., 44 (1), pp. 82-101 | ||
| 504 | |a Araya, R., Barrenechea, G.R., Poza, A., An adaptive stabilized finite element method for the generalized Stokes problem (2008) J. Comput. Appl. Math., 214, pp. 457-479 | ||
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| 504 | |a Boffi, D., Brezzi, F., Demkowicz, L., Durán, R.G., Falk, R., Fortin, M., (2008) Mixed Finite Elements, Compatibility Conditions, and Applications, Lectures Notes in Mathematics, 1939 | ||
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| 504 | |a Bochev, P.B., Dohrmann, C.R., A computational study of stabilized, low-order C0 finite element approximations of Darcy equations (2006) Comput. Mech., 38, pp. 323-333 | ||
| 504 | |a Brunner, F., Radu, F., Knabner, P., Analysis of upwind-mixed hybrid finite element method for transport problems (2014) SIAM J. Numer. Anal., 52 (1), pp. 1938-1953 | ||
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| 520 | 3 | |a In this paper we analyze a low-order family of mixed finite element methods for the numerical solution of the Stokes problem and a second order elliptic problem, in two space dimensions. In these schemes, the pressure is interpolated on a mesh of rectangular elements, while the velocity is approximated on a triangular mesh obtained by dividing each rectangle into four triangles by its diagonals. For the lowest order P1Q0, a global spurious pressure mode is shown to exist and so this element, as P1Q1 case analyzed in Armentano and Blasco (2010), is unstable. However, following the ideas given in Bochev et al. (2006), a simple stabilization procedure can be applied, when we approximate the solution of the Stokes problem, such that the new P1Q0 and P1Q1 methods are unconditionally stable, and achieve optimal accuracy with respect to solution regularity with simple and straightforward implementations. Moreover, we analyze the application of our P1Q1 element to the mixed formulation of the elliptic problem. In this case, by introducing the modified mixed weak form proposed in Brezzi et al. (1993), optimal order of accuracy can be obtained with our stabilized P1Q1 elements. Numerical results are also presented, which confirm the existence of the spurious pressure mode for the P1Q0 element and the excellent stability and accuracy of the new stabilized methods. © 2017 Elsevier B.V. |l eng | |
| 536 | |a Detalles de la financiación: Universidad de Buenos Aires, UBACyT 20020130100205BA | ||
| 536 | |a Detalles de la financiación: Agencia Nacional de Promoción Científica y Tecnológica, PICT 2014-1771 | ||
| 536 | |a Detalles de la financiación: Consejo Nacional de Investigaciones Científicas y Técnicas, PIP 11220130100184CO | ||
| 536 | |a Detalles de la financiación: This work is devoted to the memory of Jordi Blasco. The author’s work was supported by ANPCyT under grant PICT 2014-1771 , CONICET under grant PIP 11220130100184CO and by Universidad de Buenos Aires under grant UBACyT 20020130100205BA . | ||
| 593 | |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, IMAS-Conicet, Buenos Aires, 1428, Argentina | ||
| 690 | 1 | 0 | |a CROSS-GRID ELEMENTS |
| 690 | 1 | 0 | |a ELLIPTIC PROBLEMS |
| 690 | 1 | 0 | |a MIXED FINITE ELEMENTS |
| 690 | 1 | 0 | |a STABILITY ANALYSIS |
| 690 | 1 | 0 | |a STOKES PROBLEM |
| 690 | 1 | 0 | |a COMPUTATIONAL MECHANICS |
| 690 | 1 | 0 | |a MESH GENERATION |
| 690 | 1 | 0 | |a NAVIER STOKES EQUATIONS |
| 690 | 1 | 0 | |a NUMERICAL METHODS |
| 690 | 1 | 0 | |a STABILIZATION |
| 690 | 1 | 0 | |a ELLIPTIC PROBLEM |
| 690 | 1 | 0 | |a GRID ELEMENTS |
| 690 | 1 | 0 | |a MIXED FINITE ELEMENTS |
| 690 | 1 | 0 | |a STABILITY ANALYSIS |
| 690 | 1 | 0 | |a STOKES PROBLEM |
| 690 | 1 | 0 | |a FINITE ELEMENT METHOD |
| 773 | 0 | |d Elsevier B.V., 2018 |g v. 330 |h pp. 340-355 |p J. Comput. Appl. Math. |x 03770427 |w (AR-BaUEN)CENRE-1107 |t Journal of Computational and Applied Mathematics | |
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| 856 | 4 | 0 | |u https://doi.org/10.1016/j.cam.2017.09.002 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_03770427_v330_n_p340_Armentano |y Handle |
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