We consider two dimensional inverse steady state heat conduction
problems in complex geometries. The coefficients of the elliptic
equation are assumed to be non-constant. Cauchy data are given along
part of the boundary, and we want to find the solution in the whole
domain. Using an orthogonal coordinate transformation the domain is
mapped on a rectangle. The Cauchy problem can then be stabilized by
replacing one derivative by a bounded approximation. That well-posed
problem is solved numerically using a method of lines. Numerical
examples are given and an industrial application is described.
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