Abstract
A local a posteriori error indicator for the well known Morley element for the Kirchhoff plate bending problem is presented. The error indicator is proven to be both reliable and efficient. The technique applied is general and it is shown to have also other applications.
Similar content being viewed by others
References
Agmon S. (1965). Lectures on Elliptic Boundary Value Problems. Van Nostrand, Princeton
Beirão da Veiga, L., Niiranen, J., Stenberg, R.: A family of C 0 finite elements for Kirchhoff plates. Helsinki University of Technology, Insitute of Mathematics, Research Reports A483, http://math.tkk.fi/reports. Espoo (2005)
Brenner S.C. and Scott L.R. (1994). The Mathematical Theory of Finite Element Methods. Springer, Berlin
Brezzi F. and Fortin M. (1991). Mixed and Hybrid Finite Element Methods. Springer, New York
Carstensen C., Bartels S. and Jansche S. (2002). A posteriori error estimates for nonconforming finite element methods. Numer. Math. 92: 233–256
Carstensen C. and Dolzmann G. (1998). A posteriori error estimates for mixed FEM in elasticity. Numer. Math. 81: 187–209
Carstensen, C., Hu, J., Orlando, A.: Framework for the a posteriori error analysis of nonconforming finite elements. Preprint 2005-11, Insitut für Mathematik, Humboldt-Universität zu Berlin, http://www.mathematik.hu-berlin.de/publ/pre/2005/P-05-11.pdf
Charbonneau A., Dossou K. and Pierre R. (1997). A residual-based a posteriori error estimator for the Ciarlet-Raviart formulation of the first biharmonic problem. Numer. Meth. Part. Differ. Equ. 13: 93–111
Ciarlet P.G. (1978). The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam
Clément P. (1975). Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9: 77–84
Dari E., Duran R., Padra C. and Vampa V. (1996). A posteriori error estimators for nonconforming finite element methods. Math. Mod. Numer. Anal. 30: 385–400
Kanshat G. and Suttmeier F.-T. (1999). A posteriori error estimates for nonconforming finite element schemes. CALCOLO 36: 129–141
Ming, W., Xu, J.: The Morley element for fourth order elliptic equations in any dimensions. Numer. Math. Online First (2006)
Morley L.S.D. (1968). The triangular equilibrium element in the solution of plate bending problems. Aero. Quart. 19: 149–169
Rannacher R. and Turek S. (1992). Simple Nonconforming Quadrilateral Stokes Element. Num. Methods Part. Diff. Equ. 8: 97–111
Shi Z.C. (1990). Error estimates for the Morley element. Chin. J. Numer. Math. Appl. 12: 102–108
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
da Veiga, L.B., Niiranen, J. & Stenberg, R. A posteriori error estimates for the Morley plate bending element. Numer. Math. 106, 165–179 (2007). https://doi.org/10.1007/s00211-007-0066-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00211-007-0066-1