Even-odd goal-oriented a posteriori error estimation for elliptic problems

In this paper we study several goal-oriented error estimates based on the standard even-odd a posteriori error estimates for elliptic problems. We present four goal-oriented estimates and prove that Oden's estimate converges to the true error under mesh refinement. Computational results further indicate that Oden's estimate converges to the true error under even-p refinement. We also extend Oden's procedure to fourth-order problems using even-odd error estimates and prove its asymptotic exactness under mesh refinement.