Seminar on Qualitative Theory of Differential Equations - Patrik Mihala (30.10.2025)

Thursday 30.10.2025 at 14:00, Lecture room M 223

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Patrik Mihala:
Fully Implicit Finite-Volume Method for Doubly-Nonlinear Diffusion in Two-Component Domain

Abstract:
This work models diffusion in two adjoining regions governed by a doubly nonlinear diffusion law. The regions are coupled across their common interface by continuity of the normal flux and a nonlinear Nernst-type relation. In the simulations we use a conservative finite-volume discretization in space and fully implicit time stepping with adaptive step sizes and adaptive damping. The interface condition is approximated by a penalty formulation. The resulting nonlinear system is solved by Newton's method with an analytic Jacobian. The experiments show close agreement with a validated explicit scheme with approximately half the computational time, successful computation of a stiff case that explicit scheme cannot compute, and long-time relaxation with a stable interface jump.

This is a joint work with J. Filo and J. Babušíková.

 

 

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