| Abstract: |
| We consider finite element approximation in the context of the ill-posed elliptic unique continuation problem, and introduce a notion of optimal error estimates that includes convergence with respect to a mesh parameter and perturbations in data. The rate of convergence is determined by the conditional stability of the underlying continuous problem and the polynomial order of the finite element approximation space. We present a stabilized finite element method satisfying the optimal estimate, and discuss a proof showing that no finite element approximation can converge at a better rate. |
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