✦ LIBER ✦
Numerical analysis of an energy-like minimization method to solve the Cauchy problem with noisy data
✍ Scribed by R. Rischette; T.N. Baranger; N. Debit
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 516 KB
- Volume
- 235
- Category
- Article
- ISSN
- 0377-0427
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✦ Synopsis
This paper is concerned with solving the Cauchy problem for an elliptic equation by minimizing an energy-like error functional and by taking into account noisy Cauchy data. After giving some fundamental results, numerical convergence analysis of the energy-like minimization method is carried out and leads to adapted stopping criteria for the minimization process depending on the noise rate. Numerical examples involving smooth and singular data are presented.