删除或更新信息,请邮件至freekaoyan#163.com(#换成@)

四维空间上的C1单纯形有限元族

本站小编 Free考研考试/2021-12-27

张上游
特拉华大学, DE 19716, 美国
收稿日期:2016-01-12出版日期:2016-08-15发布日期:2016-09-08




A FAMILY OF DIFFERENTIABLE FINITE ELEMENTS ON SIMPLICIAL GRIDS IN FOUR SPACE DIMENSIONS

Zhang Shangyou
Department of Mathematical Sciences, University of Delaware, DE 19716, USA
Received:2016-01-12Online:2016-08-15Published:2016-09-08







摘要



编辑推荐
-->


我们基于四维空间一般单纯形网格构造了一族可微的分片kk>=17)次多项式有限元.这类光滑有限元空间具有最优阶逼近性.作为副产品,我们得到一族三维的四面体网格上C2-Pk有限元.
MR(2010)主题分类:
65M60
65N30

分享此文:
C1单纯形有限元族”的文章,特向您推荐。请打开下面的网址:http://www.computmath.com/jssx/CN/abstract/abstract310.shtml' name="neirong">C1单纯形有限元族'>

()

[1] Alfeld P and Sirvent M. The structure of multivariate superspline spaces of high degree[J]. Math. Comp., 1991, 57(195):299-308.

[2] Argyris J H, Fried I, Scharpf D W. The TUBA family of plate elements for the matrix displacement method[J]. The Aeronautical Journal of the Royal Aeronautical Society, 1968, 72:514-517.

[3] Bell K. A refined triangular plate bending element[J]. Internal. J. Numer. methods Engrg, 1969, 1:101-122.

[4] Bogner F K, Fox R L and Schmit L A. The generation of interelement compatible stiffness and mass matrices by the use of interpolation formulas. Proceedings of the conference on Matrix Methods in Structural Mechanics, Wright Patterson A.F.B. Ohio, 1965.

[5] Ciarlet P G. The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978.

[6] Douglas Jr J, Dupont T, Percell P, Scott R. A family of C1 finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems[J]. RAIRO Anal. Numer., 1979, 13:227-255.

[7] Fraeijs de Veubeke B. A conforming finite element for plate bending. in:O.C. Zienkiewicz and G.S. Holister (Eds.), Stress Analysis, Wiley, New York, 1965, 145-197.

[8] Heindl G. Interpolation and approximation by piecewise quadratic C1-functions of two variables[J]. International Schriftenreihe Numerical Mathematics, 1979, 51:146-161.

[9] Hu J, Huang Y and Zhang S. The lowest order differentiable finite element on rectangular grids[J]. SIAM J. Numer. Anal., 2011, 49(4):1350-1368.

[10] Hu J and Zhang S. The minimal conforming Hk finite element spaces on Rn rectangular grids[J]. Math. Comp., 2015, 84(292):563-579.

[11] Lai M J and Schumaker L L. On the approximation power of bivariate splines[J]. Adv. in Comp. Math., 1998, 9:251-279.

[12] Morgan J, Scott L R. A nodal basis for C1 piecewise polynomials of degree n[J]. Math. comp., 1975, 29:736-740.

[13] Morley L S D. The triangular equilibrium element in the solution of plate bending problems[J]. Aero. Quart., 1968, 19:149-169.

[14] Percell P. On cubic and quartic Clough-Tocher finite elements[J]. SIAM J. Numer. Anal., 1976, 13:100-103.

[15] Powell M J D, Sabin M A. Piecewise quadratic approximations on triangles[J]. ACM Transactions on Mathematical Software, 1977, 3-4:316-325.

[16] Ruas V. A quadratic finite element method for solving biharmonic problems in Rn[J]. Numer. Math., 1988, 52:33-43.

[17] Sander G. Bornes supérieures et inférieures dans l'analyse matricielle des plaques en flexion-torsion[J]. Bull. Sco. Roy. Sci. Liége, 1964, 33:456-494.

[18] Schumaker L L. On super splines and finite elements[J]. SIAM J. Numer. Anal., 1989, 26:997-1005.

[19] Schumaker L L and Sorokina T. C1 quintic splines on type-4 tetrahedral partitions[J]. Adv. in Comp. Math., 2004, 21:421-444.

[20] Sorokina T and Worsey A J. A multivariate Powell-Sabin interpolant[J]. Adv. Comput. Math.,2008, 29(1):71-89.

[21] Sorokina T. C1 multivariate Clough-Tocher interpolant[J]. Constr. Approx., 2009, 29(1):41-59.

[22] Sorokina T. A C1 cross polytope macro-element in four variables. Approximation theory XI:Gatlinburg 2004, 405-422, Mod. Methods Math., Nashboro Press, Brentwood, TN, 2005.

[23] Wang M and Xu J. The Morley element for fourth order elliptic equations in any dimensions[J]. Numer. Math., 2006, 103(1):155-169.

[24] Wang M, Shi Z C and Xu J. Some n-rectangle nonconforming finite elements for fourth order elliptic equations[J]. J. Comput. Math., 2007, 25(4):408-420.

[25] Wang M, Shi Z C and Xu J. A new class of Zienkiewicz-type non-conforming element in any dimensions[J]. Numer. Math., 2007, 106:335-347.

[26] Yang Y, Lin F and Zhang Z. N-simplex Crouzeix-Raviart element for the second-order elliptic/eigenvalue problems[J]. Int. J. Num. Anal. Mod., 2009, 6(4):615-626.

[27] ?enišek A. Interpolation polynomials on the triangle[J]. Numer. Math., 1970, 15:283-296.

[28] ?enišek A. Polynomial approximation on tetrahedrons in the finite element method[J]. J. Approximation Theory, 1973, 7:334-351.

[29] ?enišek A. A general theorem on triangular Cm elements[J]. RAIROModel. Math. Anal. Numer., 1974, 22:119-127.

[30] Zhang S. A family of 3D continuously differentiable finite elements on tetrahedral grids[J]. Applied Numer. Math., 2009, 59(1):219-233.

[31] Zhang S. On the full C1-Qk finite element spaces on rectangles and cuboids[J]. Adv. Appl. Math. Mech., 2010, 2(6):701-721.

[1]唐斯琴, 李宏, 董自明, 赵智慧. 对流反应扩散方程的稳定化时间间断时空有限元解的误差估计[J]. 计算数学, 2020, 42(4): 472-486.
[2]洪庆国, 刘春梅, 许进超. 一种抽象的稳定化方法及在非线性不可压缩弹性问题上的应用[J]. 计算数学, 2020, 42(3): 298-309.
[3]刘阳, 李金, 胡齐芽, 贾祖朋, 余德浩. 边界元方法的一些研究进展[J]. 计算数学, 2020, 42(3): 310-348.
[4]戴小英. 电子结构计算的数值方法与理论[J]. 计算数学, 2020, 42(2): 131-158.
[5]关宏波, 洪亚鹏. 抛物型界面问题的变网格有限元方法[J]. 计算数学, 2020, 42(2): 196-206.
[6]何斯日古楞, 李宏, 刘洋, 方志朝. 非稳态奇异系数微分方程的时间间断时空有限元方法[J]. 计算数学, 2020, 42(1): 101-116.
[7]张然. 弱有限元方法在线弹性问题中的应用[J]. 计算数学, 2020, 42(1): 1-17.
[8]李世顺, 祁粉粉, 邵新平. 求解定常不可压Stokes方程的两层罚函数方法[J]. 计算数学, 2019, 41(3): 259-265.
[9]王俊俊, 李庆富, 石东洋. 非线性抛物方程混合有限元方法的高精度分析[J]. 计算数学, 2019, 41(2): 191-211.
[10]葛志昊, 葛媛媛. 几乎不可压线弹性问题的新的Uzawa型自适应有限元方法[J]. 计算数学, 2018, 40(3): 287-298.
[11]武海军. 高波数Helmholtz方程的有限元方法和连续内罚有限元方法[J]. 计算数学, 2018, 40(2): 191-213.
[12]葛志昊, 吴慧丽. 体积约束的非局部扩散问题的后验误差分析[J]. 计算数学, 2018, 40(1): 107-116.
[13]张纯禹, 陈恭, 王一正, 王烨. 快速求解参数化偏微分方程的缩减基有限元方法及其在核工程中的应用[J]. 计算数学, 2017, 39(4): 431-444.
[14]李宏, 杜春瑶, 赵智慧. 反应扩散方程的连续时空有限元方法[J]. 计算数学, 2017, 39(2): 167-178.
[15]李晓翠, 杨小远, 张英晗. 一类随机非自伴波方程的半离散有限元近似[J]. 计算数学, 2017, 39(1): 42-58.

--> -->
阅读次数
全文







摘要





Cited

Shared






PDF全文下载地址:

http://www.computmath.com/jssx/CN/article/downloadArticleFile.do?attachType=PDF&id=310
相关话题/计算 数学 推荐 结构 阅读