zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Efficient rectangular mixed finite elements in two and three space variables. (English) Zbl 0689.65065
Summary: Two families of mixed finite elements for second order elliptic equations are introduced, one in two variables and the other in three. These rectangular elements are related to ones in two space and in three space studied earlier by the authors. They give the same rates of convergence as the corresponding Raviart-Thomas elements with fewer parameters per rectangle. Hybridization of the mixed method for these elements is considered, and alternating-direction iterative techniques are discussed.

MSC:
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
35J25Second order elliptic equations, boundary value problems
WorldCat.org
Full Text: EuDML
References:
[1] [1] D. N. ARNOLD and F. BREZZI, Mixed and nonconforming finite element methods : implementation, postprocessing, and error estimates, R. A. I. R. O. Mathematical Modelling and Numerical Analysis 19 (1985), pp. 7-32. Zbl0567.65078 MR813687 · Zbl 0567.65078 · eudml:193443
[2] [2] I. BABUSKA, The finite element with Lagrangian multipliers, Numer. Math. 20 (1973), pp. 179-192. Zbl0258.65108 MR359352 · Zbl 0258.65108 · doi:10.1007/BF01436561 · eudml:132183
[3] J. H. BRAMBLE and A. H. SCHATZ, Higher order local acuracy by averaging in the finite element method, Math. of Comp. 31 (1977), pp. 94-111. Zbl0353.65064 MR431744 · Zbl 0353.65064 · doi:10.2307/2005782
[4] [4] J. H. BRAMBLE and A. H. SCHATZ, Estimates for spline projections, R.A.I.R.O. Anal. numér. 10 (1976), pp. 5-37. Zbl0343.65045 MR436620 · Zbl 0343.65045 · eudml:193279
[5] [5] F. BREZZI, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers, R.A.I.R.O. Anal. numér. R2 (1974), pp. 129-151. Zbl0338.90047 MR365287 · Zbl 0338.90047 · eudml:193255
[6] [6] F. BREZZI, J. Jr. DOUGLAS, R. DURAN and M. FORTIN, Mixed finite elements for second order elliptic problems in three variables, to appear in Numer. Math. Zbl0631.65107 MR890035 · Zbl 0631.65107 · doi:10.1007/BF01396752 · eudml:133194
[7] [7] F. BREZZI, J. Jr. DOUGLAS and L. D. MARINI, Two families of mixed finite elements for second order elliptic problems, Numer. Math. 47 (1985), pp. 217-235. Zbl0599.65072 MR799685 · Zbl 0599.65072 · doi:10.1007/BF01389710 · eudml:133032
[8] F. BREZZI, J. Jr. DOUGLAS and L. D. MARINI, Variable degree mixed methods for second order elliptic problems, Matematica Aplicada e Computacional 4 (1985), pp. 19-34. Zbl0592.65073 MR808322 · Zbl 0592.65073
[9] D. C. BROWN, Alternating-direction iterative schemes for mixed finite element methods for second order elliptic problems, Thesis, University of Chicago, 1982.
[10] [10] J. Jr. DOUGLAS, Alternating direction methods for three space variables, Numer. Math. 4 (1962), pp. 42-65. Zbl0104.35001 MR136083 · Zbl 0104.35001 · doi:10.1007/BF01386295 · eudml:131514
[11] J. Jr. DOUGLAS, R. DURAN and P. PIETRA, Formulation of alternating-direction iterative methods for mixed methods in three space, to appear in the proceedings of the Symposium Internacional de Analisis Numérico, Madrid, September 1985. Zbl0609.65071 MR899777 · Zbl 0609.65071
[12] J. Jr. DOUGLAS, R. DURAN and P. PIETRA, Alternating-direction iteration for mixed finite element methods, to appear in Computing Methods in Applied Science and Engineering VII (R. Glowinski and J. L. Lions, eds.), North-Holland, 1986. Zbl0677.65105 MR905295 · Zbl 0677.65105
[13] [13] J. Jr. DOUGLAS and F. MILNER, Interior and superconvergence estimates for mixed methods for second order elliptic problems, R.A.I.R.O. Mathematical Modelling and Numerical Analysis 19 (1985), pp. 397-428. Zbl0613.65110 MR807324 · Zbl 0613.65110 · eudml:193453
[14] J. Jr. DOUGLAS and P. PIETRA, A description of some alternating-direction iterative techniques for mixed finite element methods, to appear in the proceedings of a SIAM/SEG/SPE conference, Houston, January 1985.
[15] J. Jr. DOUGLAS and P. PIETRA, private communication.
[16] J. Jr. DOUGLAS and , Global estimates for mixed methods for second order elliptic equations, Math. of Comp. 44 (1985), pp. 39-52. Zbl0624.65109 MR771029 · Zbl 0624.65109 · doi:10.2307/2007791
[17] [17] M. FORTIN, An analysis of the convergence of mixed finite element methods, R.A.I.R.O. Anal, numér. 11 (1977), pp. 341-354. Zbl0373.65055 MR464543 · Zbl 0373.65055 · eudml:193306
[18] B. X. FRAEIJS DE VEUBEKE, Displacement and equilibrium models in the finite element method, Stress Analysis (O. C. Zienkiewicz and G. Holister, eds.), Wiley, New York, 1965. · Zbl 0359.73007
[19] B. X. FRAEIJS DE VEUBEKE, Stress function approach, World Congress on the Finite Element Method in Structural Mechanics, Bournemouth, 1975. Zbl0404.73076 · Zbl 0404.73076
[20] Handbook of Mathematical Functions (M. Abromowitz and I. Stegun, eds.), Chapter 22 (O. W. Hochstrasser).
[21] P. A. RAVIART and J. M. THOMAS, A mixed finite element method for 2nd order elliptic problems, Mathematical Aspects of the Finite Element Method, Lecture Notes in Mathematics 606, Springer, Berlin-Heidelberg-New York, 1977. Zbl0362.65089 MR483555 · Zbl 0362.65089
[22] J. M. THOMAS, Sur l’analyse numérique des méthodes d’éléments finis hybrides et mixtes, Thèse, Université P.-et-M. Curie, Paris, 1977.