Abstract
Numerical Solution of Cauchy Problems for Elliptic PDE's in Complex Geometries
Lars Elde'n
Linkoping University, Sweden
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.
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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