We study the mixed finite element approximation of the second order elliptic problem with gradient nonlinearities in two and three space dimensions. Existence and uniqueness of the approximate solution are proved and optimal order a priori error estimates in Lm(Ω) are obtained. Also, reliable and efficient a posteriori error estimators measured in the L m(Ω)-norm are derived. Numerical examples are provided to illustrate the performance of the proposed estimator.
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics