Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
Stabilization of explicit methods for convection diffusion equations by discrete mollification
Computers & Mathematics with Applications
Approximate solution of hyperbolic conservation laws by discrete mollification
Applied Numerical Mathematics
Identification of source terms in 2-D IHCP
Computers & Mathematics with Applications
Source term identification in 1-D IHCP
Computers & Mathematics with Applications
Solving the inverse problem of identifying an unknown source term in a parabolic equation
Computers & Mathematics with Applications
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The discrete mollification method is a convolution-based filtering procedure suitable for the regularization of ill-posed problems. Combined with explicit space-marching finite difference schemes, it provides stability and convergence for a variety of coefficient identification problems in linear parabolic equations. In this paper, we extend such a technique to identify some nonlinear diffusion coefficients depending on an unknown space dependent function in one dimensional parabolic models. For the coefficient recovery process, we present detailed error estimates and to illustrate the performance of the algorithms, several numerical examples are included.