Pointwise a posteriori error estimates for monotone semi-linear equations

Adams R.A. Sobolev Spaces, vol. 65 of Pure and Applied Mathematics. Academic Press, Inc., a subsidiary of Harcourt Brace Jovanovich, Publishers, New York, San Francisco, London (1975) Ainsworth M., Oden J.T. (2000) A Posteriori Error Estimation in Finite Element Analysis. Wiley, New York Alt H.W., Phillips D. (1986) A free boundary problem for semilinear elliptic equations. J. Reine Angew. Math. 368, 63–107 Arnold, D.N., Mukherjee, A., Pouly, L.: Adaptive finite elements and colliding black holes. Numerical analysis 1997 (Dundee), 1–15, Pitman Res. Notes Math. Ser., 380, Longman, Harlow (1998) Babuška I., Rheinboldt W. (1978) Error estimates for adaptive finite element computations. SIAM J. Numer. Anal. 15, 736–754 Brenner S.C., Scott L.R. (2002) The mathematical theory of finite element methods. Springer, Berlin Heidelberg New York Brezis H., Strauss W. (1973) Semilinear second-order elliptic equations in L 1. J. Math. Soc. Japan, 25, 565–590 Callegari A.J., Nachman A. (1980) A nonlinear singular boundary value problem in the theory of pseudoplastic fluids. SIAM J. Appl. Math. 30, 275–281 Ciarlet P.G. (1980) The finite element method for elliptic problems. North-Holland, Amsterdam Dari E., Durán R.G., Padra C. (2000) Maximum norm error estimators for three-dimensional elliptic problems. SIAM J. Numer. Anal. 37, 683–700 Evans L.C. (1998) Partial differential equations. In: Humphreys J.E., Saltman D.J., Sattinger D., Shaneson J.L., (eds) Graduate Studies in Mathematics, vol 19. AMS, Providence Gilbarg D., Trudinger N.S. (1983) Elliptic partial diffferential equations of second order. Springer, Berlin Heidelberg New York Grisvard P. (1985) Elliptic problems in nonsmooth domains. Pitman, London Henson V.E., Shaker A.W. (1996) Theory and numerics for a semilinear PDE in the theory of pseudoplastic fluids. Appl. Anal. 63, 271–285 Kinderlehrer D., Stampacchia G. (1980) An introduction to variational inequalities and their applications vol 88 of Pure Appl Math. Academic, New York Lazer A.C., McKenna P.J. (1991) On a singular nonlinear elliptic boundary value problem. Proc. AMS 111, 721–730 Nochetto R.H. (1995) Pointwise a posteriori error estimates for elliptic problems on highly graded meshes. Math. Comp. 64, 1–22 Nochetto R.H. (1988) Sharp L ∞-error estimates for semilinear elliptic problems with free boundaries. Numer. Math. 54, 243–255 Nochetto R.H., Siebert K.G., Veeser A. (2003) Pointwise a~posteriori error control for elliptic obstacle problems. Numer. Math. 95, 163–195 Nochetto R.H., Siebert K.G., Veeser A. (2005) Fully localized a posteriori error estimators and barrier sets for contact problems. SIAM J. Numer. Anal. 42, 2118–2135 Ortega J.M., Rheinboldt W.C. (1970) Iterative solution of nonlinear equations in several variables. Academic, New York Phillips D. (1983) Hausdorff measure estimates of a free boundary for a minimum problem. Comm. Partial Differ. Equ. 8, 1409–1454 Richardson W.B. Jr. (2000) Sobolev preconditioning for the Poisson-Boltzmann equation. Comput. Meth. Appl. Mech. Eng. 181, 425–436 Schmidt A., Siebert K.G. (2005) Design of adaptive finite element software: the finite element toolbox ALBERTA. LNCSE Series, vol 42. Springer, Berlin Heidelberg New York Schmidt A., Siebert K.G. (2001) ALBERT – Software for scientific computations and applications. Acta Math. Univ. Comenianae 70, 105–122 Verfürth R. (1996) A review of a posteriori error estimation and adaptive mesh-refinement techniques. Wiley, Teubner