Identification of the diffusion in a nonlinear parabolic problem and numerical resolution

Sameh Abidi, Jamil Satouri
2016 ANZIAM Journal  
This paper presents an iterative method to identify the diffusion in a semi-linear parabolic problem. This method can be generalized to other kind of problems, elliptic, parabolic and hyperbolic in twodimensional and three-dimensional case. The diffusion is obtained by solving an optimal control problem. By imposing specific conditions to the data, we build a sequence of linear problems which converge to the exact solution. We discretize our problem by a finite element method in the first case
more » ... nd a spectral method in the second case, using the sensibility method for approximating the gradient of the functional. Some numerical experiments prove the efficiency of this method.
doi:10.21914/anziamj.v57i0.8835 fatcat:jl74qjwdkncczihhduu5ni5qe4