We develop implicit a posteriori error estimators for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedures. Convergence properties of the implicit error estimator are discussed independently of residual type error estimators, and this gives a freedom in the choice of boundary conditions. General assumptions are elaborated for the gradient averaging which define a family of implicit a posteriori error estimators. We will demonstrate the performance and the favor of the method through numerical experiments.
- A posteriori error analysis
- Gradient recovery
- Implicit methods
Horváth, T. L., & Izsak, F. (2012). Implicit a posteriori error estimation using patch recovery techniques. Central European journal of mathematics, 10(1), 55-72. https://doi.org/10.2478/s11533-011-0119-7