Data Oscillation and Convergence of Adaptive FEM
SIAM Journal on Numerical Analysis
Adaptive Finite Element Methods with convergence rates
Numerische Mathematik
Optimality of a Standard Adaptive Finite Element Method
Foundations of Computational Mathematics
A Goal-Oriented Adaptive Finite Element Method with Convergence Rates
SIAM Journal on Numerical Analysis
Quasi-Optimal Convergence Rate of an Adaptive Discontinuous Galerkin Method
SIAM Journal on Numerical Analysis
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We propose a new goal-oriented adaptive finite element method, which is based on the weighting of the residuals from the primal and dual problem at each step of the iteration. Our main result is the quasi-optimality of the resulting algorithm. Numerical experiments are reported, showing the convergence behavior of the algorithm.