Error analysis in the reconstruction of a convolution kernel in a semilinear parabolic problem with integral overdetermination

• Autores: R.H. De Staelen, K. Van Bockstal, Marián Slodicka
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 275, Nº 1, 2015, págs. 382-391
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.06.026
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• Resumen

  • A semilinear parabolic problem of second order with an unknown solely time-dependent convolution kernel is considered. An additional given global measurement (a space integral of the solution) ensures the existence of a unique weak solution. The unknown kernel function can be approximated by a time-discrete numerical scheme based on Backward Euler�s method (Rothe�s method). In this contribution, an error analysis for the time discretization is performed of the existing numerical algorithm. Numerical experiments support the theoretically obtained results.