Recovering the Boundary Data in the Two Dimensional Inverse Heat Conduction Problem Using the Ritz-Galerkin Method

This article presents a numerical method to find the
heat flux in an inhomogeneous inverse heat conduction problem with
linear boundary conditions and an extra specification at the terminal.
The method is based upon applying the satisfier function along with
the Ritz-Galerkin technique to reduce the approximate solution of the
inverse problem to the solution of a system of algebraic equations.
The instability of the problem is resolved by taking advantage of
the Landweber’s iterations as an admissible regularization strategy.
In computations, we find the stable and low-cost results which
demonstrate the efficiency of the technique.

Authors:

• Saeed Sarabadan
• Kamal Rashedi

Keywords:

• Inverse problem
• parabolic equations
• heat equation
• Ritz-Galerkin method
• Landweber iterations.

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