Karlstad Applied Analysis Seminar (KAAS)

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Future seminars:

TALK 164

When: 6th of October 2026, 10:40-11:30
What:  A new convergence proof of an iterative method for elliptic Cauchy problems
Who: Abhijit Guchhait, Karlstad University, Sweden
Where: 1D 262 (offline)  and online: https://kau-se.zoom.us/j/61616693592

We consider an elliptic Cauchy problem for the Poisson equation in which both Dirichlet and Neumann boundary data are prescribed only on a portion of the boundary, while no boundary conditions are available on the remaining part of the boundary. Such problems are typically ill-posed, making the development of stable and computationally efficient methods challenging. In this work, we investigate an iterative approach based on alternating Dirichlet and Neumann boundary conditions. The proposed scheme is formulated within a Hilbert space framework, where each iteration can be interpreted as an orthogonal projection onto an appropriate closed subspace. This orthogonal formulation provides a clear geometric interpretation of the algorithm and allows its convergence properties to be established through the theory of alternating projections. Our analysis gives insight into the behavior of the iterative  process and provides a systematic framework for studying convergence.

This is joint work with Martin Lind and Adrian Muntean (Karlstad, Sweden). The work is fully funded by the Swedish Research Council for the project "Homogenization of Nonlinear Drift-diffusion Systems for Charge Transport through Bicontinuous Media" (Grant No. 2024-05606).