Two and three dimensional H2 2-conforming finite element approximations without C 1-elements

被引：3

作者：

Ainsworth, Mark ^{[1
]}

Parker, Charles ^{[2
]}

机构：

[1] Brown Univ, Div Appl Math, Box F,182 George St, Providence, RI 02912 USA

[2] Univ Oxford, Math Inst, Andrew Wiles Bldg,Woodstock Rd, Oxford OX2 6GG, England

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2024年 / 431卷

基金：

美国国家科学基金会;

关键词：

H2-conforming finite elements; C1 finite elements; SPACES; EQUATIONS; BOUNDARY; PART; INTERPOLATION; INTEGRATION; TRACES; FAMILY; ENERGY;

D O I：

10.1016/j.cma.2024.117267

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We develop a method to compute H2 2-conforming finite element approximations in both two and three space dimensions using readily available finite element spaces. This is accomplished by deriving a novel, equivalent mixed variational formulation involving spaces with at most H1 1-smoothness, so that conforming discretizations require at most C0 0-continuity. The method is demonstrated on arbitrary order C1 1-splines.

引用

页数：24

共 55 条

[1] COMPUTING H2-CONFORMING FINITE ELEMENT APPROXIMATIONS WITHOUT HAVING TO IMPLEMENT C1-ELEMENTS [J].

Ainsworth, Mark ;

Parker, Charles .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2024, 46 (04) :A2398-A2420

[2] Unlocking the secrets of locking: Finite element analysis in planar linear elasticity [J].

Ainsworth, Mark ;

Parker, Charles .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2022, 395

[3] AN EXPLICIT BASIS FOR C1 QUARTIC BIVARIATE SPLINES [J].

ALFELD, P ;

PIPER, B ;

SCHUMAKER, LL .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1987, 24 (04) :891-911

[4] Bending moment mixed method for the Kirchhoff-Love plate model [J].

Amara, M ;

Capatina-Papaghiuc, D ;

Chatti, A .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 40 (05) :1632-1649

[5] TUBA FAMILY OF PLATE ELEMENTS FOR MATRIX DISP LACEMENT METHOD [J].

ARGYRIS, JH ;

FRIED, I ;

SCHARPF, DW .

AERONAUTICAL JOURNAL, 1968, 72 (692) :701-&

[6]

Arnold D.N., 1989, ANN SCUOLA NORM-SCI, V15, P169

[7] Density results in sobolev spaces whose elements vanish on a part of the boundary [J].

Bernard, Jean-Marie Emmanuel .

CHINESE ANNALS OF MATHEMATICS SERIES B, 2011, 32 (06) :823-846

[8]

Bey J, 2000, NUMER MATH, V85, P1, DOI 10.1007/s002110000108

[9]

Boffi D., 2013, Mixed Finite Element Methods and Applications, V44, DOI [10.1007/978-3-642-36519-5, DOI 10.1007/978-3-642-36519-5]

[10]

BRAMBLE JH, 1983, RAIRO-ANAL NUMER-NUM, V17, P337

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