A posteriori error estimators for obstacle problems – another look. (English) Zbl 1118.65068

Braess, Dietrich

Numer. Math. 101, No. 3, 415-421 (2005).

Summary: We show that a posteriori estimators for the obstacle problem are easily obtained from the theory for linear equations. The theory would be even simpler if the Lagrange multiplier does not have a nonconforming contribution as it has in actual finite element computations.

MSC:

65K10	Numerical optimization and variational techniques
49J40	Variational inequalities

Keywords:

variational inequalities; elliptic obstacle problems; Lagrange multiplier; finite element

References:

[1]	Ainsworth, M., Oden, T.J.: A Posteriori Error Estimation in Finite Element Analysis. Wiley, Chichester, 2000 · Zbl 1008.65076
[2]	Bartels, Numer. Math., 99, 225 (2004) · Zbl 1063.65050
[3]	Braess, D.: Finite Elements: Theory, Fast Solvers and Applications in Solid Mechanics. Cambridge University Press, 2001 · Zbl 0976.65099
[4]	Carstensen, Math. Comp., 71, 945 (2002) · Zbl 0997.65126
[5]	Chen, Numer. Math., 84, 527 (2000) · Zbl 0943.65075
[6]	Hoppe, SIAM J. Numer. Anal., 31, 301 (1994) · Zbl 0806.65064
[7]	Kornhuber, Comput. Math. Appl., 31, 49 (1996) · Zbl 0857.65071
[8]	Suttmeier, F.T.: Consistent error estimation of FE-approximations of variational inequalities. Preprint Universität Dortmund, 2004
[9]	Veeser, SIAM J. Numer. Anal., 39, 146 (2001) · Zbl 0992.65073
[10]	Verfürth, R.: A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley-Teubner, Chichester - New York - Stuttgart, 1996 · Zbl 0853.65108