Approximation of the Biharmonic Equation by a Mixed Finite Element Method
1978; Society for Industrial and Applied Mathematics; Volume: 15; Issue: 3 Linguagem: Inglês
10.1137/0715036
ISSN1095-7170
Autores Tópico(s)Composite Structure Analysis and Optimization
ResumoPrevious article Next article Approximation of the Biharmonic Equation by a Mixed Finite Element MethodRichard S. FalkRichard S. Falkhttps://doi.org/10.1137/0715036PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract"Optimal" order of convergence estimates are derived for a new mixed element approximation for the biharmonic problem.[1] I. Babushka, The mathematical foundations of the finite element method with applications to partial differential equations, Academic Press, New York, 1972, 1–359, A. K. Aziz, ed. MR0347104 0259.00014 Google Scholar[2] Ivo Babuska, The finite element method with Lagrangian multipliers, Numer. Math., 20 (1972/73), 179–192 10.1007/BF01436561 MR0359352 0258.65108 CrossrefISIGoogle Scholar[3] James H. Bramble and , Vidar Thomée, Semidiscrete least-squares methods for a parabolic boundary value problem, Math. Comp., 26 (1972), 633–648 MR0349038 0268.65060 CrossrefISIGoogle Scholar[4] P. G. Ciarlet, Quelques méthodes d'éléments finis pour le problème d'une plaque encastréeComputing methods in applied sciences and engineering (Proc. Internat. Sympos., Versaillles, 1973), Part 1, Springer, Berlin, 1974, 156–176. Lecture Notes in Comput. Sci., Vol. 10 MR0440954 0285.65042 CrossrefGoogle Scholar[5] P. G. Ciarlet and , R. Glowinski, Dual iterative techniques for solving a finite element approximation of the biharmonic equation, Comput. Methods Appl. Mech. Engrg., 5 (1975), 277–295 10.1016/0045-7825(75)90002-X MR0373321 0305.65068 CrossrefGoogle Scholar[6] P. G. Ciarlet and , P.-A. Raviart, A mixed finite element method for the biharmonic equation, Mathematical aspects of finite elements in partial differential equations (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1974), Math. Res. Center, Univ. of Wisconsin-Madison, Academic Press, New York, 1974, 125–145. 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Maryland, Baltimore, Md., 1972), Academic Press, New York, 1972, 626–669 MR0416070 0321.65058 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails A Nitsche mixed extended finite element method for the biharmonic interface problemMathematics and Computers in Simulation, Vol. 203 Cross Ref A family of H-div-div mixed triangular finite elements for the biharmonic equationResults in Applied Mathematics, Vol. 15 Cross Ref A staggered cell-centered DG method for the biharmonic Steklov problem on polygonal meshes: A priori and a posteriori analysisComputers & Mathematics with Applications, Vol. 117 Cross Ref A stabilizer-free C0 weak Galerkin method for the biharmonic equations17 May 2022 | Science China Mathematics, Vol. 19 Cross Ref A Nitsche extended finite element method for the biharmonic interface problemComputer Methods in Applied Mechanics and Engineering, Vol. 382 Cross Ref Improved L2 and H1 error estimates for the Hessian discretization 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