Liping Liu, Michal Krizek, Mathematical Institute, Acadamy of Sciences, Zitna 25, CZ-115 67, Prague 1, Czech Republic, e-mail: krizek@beba.cesnet.cz; Pekka Neittaanmaki, Department of Mathematics, University of Jyvaskyla, P. O. Box 35, SF-40351 Jyvaskyla, Finland, e-mail: neittaanmaki@jylk.jyu.fi
Abstract: A nonlinear elliptic partial differential equation with homogeneous Dirichlet boundary conditions is examined. The problem describes for instance a stationary heat conduction in nonlinear inhomogeneous and anisotropic media. For finite elements of degree $k\ge1$ we prove the optimal rates of convergence $\Cal O(h^k)$ in the $H^1$-norm and $\Cal O(h^{k+1})$ in the $L^2$-norm provided the true solution is sufficiently smooth. Considerations are restricted to domains with polyhedral boundaries. Numerical integration is not taken into account.
Keywords: nonlinear boundary value problem, finite elements, rate of convergence, anisotropic heat conduction
Classification (MSC 1991): 65N30
