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Gradient superconvergence post-processing of the tensor-product quadratic pentahedral finite element
1. | Department of Fundamental Courses, Ningbo Institute of Technology, Zhejiang University, Ningbo, 315100, China |
2. | School of Mathematics and Computer Science, Shangrao Normal University, Shangrao, 334001, China |
References:
[1] |
I. Babuška and T. Strouboulis, The finite element method and its reliability, in Numerical Mathematics and Scientific Computation, The Clarendon Press, Oxford University Press, 2001. |
[2] |
J. H. Bramble and S. R. Hilbert, Estimation of linear functionals on Sobolev spaces with applications to Fourier transforms and spline interpolation, SIAM Journal on Numerical Analysis, 7 (1970), 112-124.
doi: 10.1137/0707006. |
[3] |
C. M. Chen, Construction Theory of Superconvergence of Finite Elements, Hunan Science and Technology Press, Changsha, 2001 (in Chinese). |
[4] |
C. M. Chen and Y. Q. Huang, High Accuracy Theory of Finite Element Methods, Hunan Science and Technology Press, Changsha, 1995 (in Chinese). |
[5] |
J. Chen and D. S. Wang, Three-dimensional finite element superconvergent gradient recovery on Par6 patterns, Numerical Mathematics: Theory, Methods and Applications, 3 (2010), 178-194.
doi: 10.4208/nmtma.2010.32s.4. |
[6] |
L. Chen, Superconvergence of tetrahedral linear finite elements, International Journal of Numerical Analysis and Modeling, 3 (2006), 273-282. |
[7] |
G. Goodsell, Pointwise superconvergence of the gradient for the linear tetrahedral element, Numerical Methods for Partial Differential Equations, 10 (1994), 651-666.
doi: 10.1002/num.1690100511. |
[8] |
Q. Lin and N. N. Yan, Construction and Analysis of High Efficient Finite Elements, Hebei University Press, Baoding, 1996 (in Chinese). |
[9] |
J. H. Liu, Superconvergence of tensor-product quadratic pentahedral elements for variable coefficient elliptic equations, Journal of Computational Analysis and Applications, 14 (2012), 745-751. |
[10] |
L. B. Wahlbin, Superconvergence in Galerkin Finite Element Methods, Lecture Notes in Mathematics vol. 1605, Springer-Verlag, Berlin, 1995. |
[11] |
Z. M. Zhang, Ultraconvergence of the patch recovery technique, Mathematics of Computation, 65 (1996), 1431-1437.
doi: 10.1090/S0025-5718-96-00782-X. |
[12] |
Z. M. Zhang, Ultraconvergence of the patch recovery technique II, Mathematics of Computation, 69 (2000), 141-158.
doi: 10.1090/S0025-5718-99-01205-3. |
[13] |
Z. M. Zhang and A. Naga, A new finite element gradient recovery method: Superconvergence property, SIAM Journal on Scientific Computing, 26 (2005), 1192-1213.
doi: 10.1137/S1064827503402837. |
[14] |
Z. M. Zhang and H. D. Victory Jr., Mathematical analysis of Zienkiewicz-Zhu's derivative patch recovery technique, Numerical Methods for Partial Differential Equations, 12 (1996), 507-524.
doi: 10.1002/(SICI)1098-2426(199607)12:4<507::AID-NUM6>3.0.CO;2-Q. |
[15] |
Z. M. Zhang and J. Z. Zhu, Analysis of the superconvergence patch recovery techniques and a posteriori error estimator in the finite element method (I), Computer Methods in Applied Mechanics and Engineering, 123 (1995), 173-187.
doi: 10.1016/0045-7825(95)00780-5. |
[16] |
Z. M. Zhang and J. Z. Zhu, Analysis of the superconvergence patch recovery techniques and a posteriori error estimator in the finite element method (II), Computer Methods in Applied Mechanics and Engineering, 163 (1998), 159-170.
doi: 10.1016/S0045-7825(98)00010-3. |
[17] |
Q. D. Zhu, High Accuracy Post-Processing Theory of the Finite Element Method, Science Press, Beijing, 2008 (in Chinese). |
[18] |
Q. D. Zhu and Q. Lin, The Superconvergence Theory of Finite Elements, Hunan Science and Technology Press, Changsha, 1989 (in Chinese). |
[19] |
O. C. Zienkiewicz and J. Z. Zhu, A simple estimator and adaptive procedure for practical engineering analysis, International Journal for Numerical Methods in Engineering, 24 (1987), 337-357.
doi: 10.1002/nme.1620240206. |
[20] |
O. C. Zienkiewicz and J. Z. Zhu, The superconvergence patch recovery and a posteriori error estimates. Part 1: The recovery techniques, International Journal for Numerical Methods in Engineering, 33 (1992), 1331-1364.
doi: 10.1002/nme.1620330702. |
[21] |
O. C. Zienkiewicz and J. Z. Zhu, The superconvergence patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity, International Journal for Numerical Methods in Engineering, 33 (1992), 1365-1382.
doi: 10.1002/nme.1620330703. |
show all references
References:
[1] |
I. Babuška and T. Strouboulis, The finite element method and its reliability, in Numerical Mathematics and Scientific Computation, The Clarendon Press, Oxford University Press, 2001. |
[2] |
J. H. Bramble and S. R. Hilbert, Estimation of linear functionals on Sobolev spaces with applications to Fourier transforms and spline interpolation, SIAM Journal on Numerical Analysis, 7 (1970), 112-124.
doi: 10.1137/0707006. |
[3] |
C. M. Chen, Construction Theory of Superconvergence of Finite Elements, Hunan Science and Technology Press, Changsha, 2001 (in Chinese). |
[4] |
C. M. Chen and Y. Q. Huang, High Accuracy Theory of Finite Element Methods, Hunan Science and Technology Press, Changsha, 1995 (in Chinese). |
[5] |
J. Chen and D. S. Wang, Three-dimensional finite element superconvergent gradient recovery on Par6 patterns, Numerical Mathematics: Theory, Methods and Applications, 3 (2010), 178-194.
doi: 10.4208/nmtma.2010.32s.4. |
[6] |
L. Chen, Superconvergence of tetrahedral linear finite elements, International Journal of Numerical Analysis and Modeling, 3 (2006), 273-282. |
[7] |
G. Goodsell, Pointwise superconvergence of the gradient for the linear tetrahedral element, Numerical Methods for Partial Differential Equations, 10 (1994), 651-666.
doi: 10.1002/num.1690100511. |
[8] |
Q. Lin and N. N. Yan, Construction and Analysis of High Efficient Finite Elements, Hebei University Press, Baoding, 1996 (in Chinese). |
[9] |
J. H. Liu, Superconvergence of tensor-product quadratic pentahedral elements for variable coefficient elliptic equations, Journal of Computational Analysis and Applications, 14 (2012), 745-751. |
[10] |
L. B. Wahlbin, Superconvergence in Galerkin Finite Element Methods, Lecture Notes in Mathematics vol. 1605, Springer-Verlag, Berlin, 1995. |
[11] |
Z. M. Zhang, Ultraconvergence of the patch recovery technique, Mathematics of Computation, 65 (1996), 1431-1437.
doi: 10.1090/S0025-5718-96-00782-X. |
[12] |
Z. M. Zhang, Ultraconvergence of the patch recovery technique II, Mathematics of Computation, 69 (2000), 141-158.
doi: 10.1090/S0025-5718-99-01205-3. |
[13] |
Z. M. Zhang and A. Naga, A new finite element gradient recovery method: Superconvergence property, SIAM Journal on Scientific Computing, 26 (2005), 1192-1213.
doi: 10.1137/S1064827503402837. |
[14] |
Z. M. Zhang and H. D. Victory Jr., Mathematical analysis of Zienkiewicz-Zhu's derivative patch recovery technique, Numerical Methods for Partial Differential Equations, 12 (1996), 507-524.
doi: 10.1002/(SICI)1098-2426(199607)12:4<507::AID-NUM6>3.0.CO;2-Q. |
[15] |
Z. M. Zhang and J. Z. Zhu, Analysis of the superconvergence patch recovery techniques and a posteriori error estimator in the finite element method (I), Computer Methods in Applied Mechanics and Engineering, 123 (1995), 173-187.
doi: 10.1016/0045-7825(95)00780-5. |
[16] |
Z. M. Zhang and J. Z. Zhu, Analysis of the superconvergence patch recovery techniques and a posteriori error estimator in the finite element method (II), Computer Methods in Applied Mechanics and Engineering, 163 (1998), 159-170.
doi: 10.1016/S0045-7825(98)00010-3. |
[17] |
Q. D. Zhu, High Accuracy Post-Processing Theory of the Finite Element Method, Science Press, Beijing, 2008 (in Chinese). |
[18] |
Q. D. Zhu and Q. Lin, The Superconvergence Theory of Finite Elements, Hunan Science and Technology Press, Changsha, 1989 (in Chinese). |
[19] |
O. C. Zienkiewicz and J. Z. Zhu, A simple estimator and adaptive procedure for practical engineering analysis, International Journal for Numerical Methods in Engineering, 24 (1987), 337-357.
doi: 10.1002/nme.1620240206. |
[20] |
O. C. Zienkiewicz and J. Z. Zhu, The superconvergence patch recovery and a posteriori error estimates. Part 1: The recovery techniques, International Journal for Numerical Methods in Engineering, 33 (1992), 1331-1364.
doi: 10.1002/nme.1620330702. |
[21] |
O. C. Zienkiewicz and J. Z. Zhu, The superconvergence patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity, International Journal for Numerical Methods in Engineering, 33 (1992), 1365-1382.
doi: 10.1002/nme.1620330703. |
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