Główne pojęcia
No approximation can converge better than the defined rate without increasing sensitivity to perturbations.
Streszczenie
The content discusses optimal finite element approximation for ill-posed elliptic problems with conditional stability. It defines optimal error estimates, introduces a class of primal-dual finite element methods, and proves the optimality of error estimates for unique continuation problems. The authors provide insights into convergence rates and sensitivity to perturbations in data.
Structure:
Introduction to Finite Element Analysis Fundamentals
Error Analysis for Ill-Posed Problems
Primal-Dual Finite Element Methods with Weakly Consistent Regularization
Proof of Optimality in Error Estimates
Key Highlights:
Cea's Lemma for Galerkin method in finite element analysis.
Approaches like Tikhonov regularization and quasi-reversibility for ill-posed problems.
Conditional stability estimates and their role in obtaining complete error estimates.
Construction of a finite element method with weakly consistent stabilization.
Statystyki
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Cytaty
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