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Finite element approximation of unique continuation of functions with finite dimensional trace
- Publication Year :
- 2023
-
Abstract
- We consider a unique continuation problem where the Dirichlet trace of the solution is known to have finite dimension. We prove Lipschitz stability of the unique continuation problem and design a finite element method that exploits the finite dimensionality to enhance stability. Optimal a priori and a posteriori error estimates are shown for the method. The extension to problems where the trace is not in a finite dimensional space, but can be approximated to high accuracy using finite dimensional functions is discussed. Finally, the theory is illustrated in some numerical examples.
- Subjects :
- Mathematics - Numerical Analysis
65N21, 35J15, 65N12, 65N20, 65N30
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2305.06800
- Document Type :
- Working Paper