Ever since the discovery of superconductivity by Heike Kamerlingh Onnes in 1911, numerous high-technological applications have been developed, including magnetic resonance imaging, superconducting cables, magnetic confinement fusion, high-energy particle accelerators, magnetic levitation, magnetic energy storage, and many more. Such technological advances are made possible by superconductors due to their fundamental properties of vanishing electrical resistance and expulsion of applied magnetic fields (Meissner effect) occurring when the temperature is cooled down below the critical temperature.

Our research project comprises the mathematical aspects of high-temperature (type-II) superconductivity governed by hyperbolic Maxwell (quasi-)variational inequalities with L1-type nonlinearities emerging from the Bean critical-state model. More details can be found in our recent works below. Check out also our poster


This project is supported by the DFG SPP 1962 (YO 159/2-1 and YO 159/2-2).

Irwin Yousept: Maxwell Quasi-Variational Inequalities in Superconductivity [PDF], ESAIM:M2AN 55 (2021) 1545-1568.

Antoine Laurain, Malte Winckler, Irwin Yousept: Shape optimization for superconductors governed by H(curl)- elliptic variational inequalities [PDF], SIAM Journal on Control and Optimization Analysis 59(3), pp. 2247--2272, 2021.

Irwin Yousept: Hyperbolic Maxwell Variational Inequalities of the Second Kind [PDF] ESAIM: COCV 26, Paper No. 34, 2020.

Malte Winckler, Irwin Yousept and Jun Zou: Adaptive edge element approximation for H(curl) elliptic variational inequalities of second kind [PDF] SIAM Journal on Numerical Analysis 58(3): 1941-1964, 2020

Malte Winckler and Irwin Yousept: Fully discrete scheme for Bean's critical-state model with temperature effects in superconductivity [PDF] SIAM Journal on Numerical Analysis 57(6): 2685–2706, 2019

Irwin Yousept:  Hyperbolic Maxwell Variational Inequalities for Bean's Critical-State Model in Type-II Superconductivity [PDF] SIAM Journal on Numerical Analysis 55(5): 2444-2464, 2017

Irwin YouseptOptimal Control of Non-Smooth Hyperbolic Evolution Maxwell Equations in Type-II Superconductivity [PDF] SIAM Journal on Control and Optimization 55(4): 2305-2332, 2017