In this paper we develop a residual based a posteriori error analysis for an augmented mixed finite element method applied to the problem of linear elasticity in the plane. More precisely, we derive a reliable and efficient a posteriori error estimator for the case of pure Dirichlet boundary conditions. In addition, several numerical experiments confirming the theoretical properties of the estimator, and illustrating the capability of the corresponding adaptive algorithm to localize the singularities and the large stress regions of the solution, are also reported.
Keywords: mixed finite element, augmented formulation, a posteriori error estimator, linear elasticity
@article{M2AN_2006__40_5_843_0, author = {Barrios, Tom\'as P. and Gatica, Gabriel N. and Gonz\'alez, Mar{\'\i}a and Heuer, Norbert}, title = {A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {843--869}, publisher = {EDP-Sciences}, volume = {40}, number = {5}, year = {2006}, doi = {10.1051/m2an:2006036}, mrnumber = {2293249}, zbl = {1109.74047}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2006036/} }
TY - JOUR AU - Barrios, Tomás P. AU - Gatica, Gabriel N. AU - González, María AU - Heuer, Norbert TI - A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2006 SP - 843 EP - 869 VL - 40 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2006036/ DO - 10.1051/m2an:2006036 LA - en ID - M2AN_2006__40_5_843_0 ER -
%0 Journal Article %A Barrios, Tomás P. %A Gatica, Gabriel N. %A González, María %A Heuer, Norbert %T A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity %J ESAIM: Modélisation mathématique et analyse numérique %D 2006 %P 843-869 %V 40 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2006036/ %R 10.1051/m2an:2006036 %G en %F M2AN_2006__40_5_843_0
Barrios, Tomás P.; Gatica, Gabriel N.; González, María; Heuer, Norbert. A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity. ESAIM: Modélisation mathématique et analyse numérique, Volume 40 (2006) no. 5, pp. 843-869. doi : 10.1051/m2an:2006036. http://www.numdam.org/articles/10.1051/m2an:2006036/
[1] PEERS: A new mixed finite element method for plane elasticity. Japan J. Appl. Math. 1 (1984) 347-367. | Zbl
, and ,[2] Error indicators for mixed finite elements in 2-dimensional linear elasticity. Comput. Method. Appl. M. 127 (1995) 345-356. | Zbl
, , , and ,[3] Mixed and Hybrid Finite Element Methods. Springer-Verlag (1991). | MR | Zbl
and ,[4] A posteriori error estimate for the mixed finite element method. Math. Comput. 66 (1997) 465-476. | Zbl
,[5] A posteriori error estimates for mixed FEM in elasticity. Numer. Math. 81 (1998) 187-209. | Zbl
and ,[6] The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, New York, Oxford (1978). | MR | Zbl
,[7] Approximation by finite element functions using local regularisation. RAIRO Anal. Numér. 9 (1975) 77-84. | Numdam | Zbl
,[8] An absolutely stabilized finite element method for the Stokes problem. Math. Comput. 52 (1989) 495-508. | Zbl
and ,[9] A note on the efficiency of residual-based a posteriori error estimators for some mixed finite element methods. Electronic Trans. Numer. Anal. 17 (2004) 218-233. | Zbl
,[10] Analysis of a new augmented mixed finite element method for linear elasticity allowing approximations. ESAIM: M2AN 40 (2006) 1-28. | Numdam
,[11] A stabilized mixed finite element method for Darcy flow. Comput. Method. Appl. M. 191 (2002) 4341-4370. | Zbl
and ,[12] Mixed and Hybrid Methods, in Handbook of Numerical Analysis II, Finite Element Methods (Part 1) P.G. Ciarlet and J.L. Lions Eds., North-Holland, Amsterdam (1991). | MR | Zbl
and ,[13] A posteriori error estimation and adaptive mesh-refinement techniques. J. Comput. Appl. Math. 50 (1994) 67-83. | Zbl
,[14] A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley-Teubner (Chichester) (1996). | Zbl
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