Workshop 2025: Time-stepping methods for projection-free approximations of evolutionary geometrically constrained partial differential equations

Session Information

Location: Lecture room Schay
Day: Thursday, 15 May
Time: 10:00 - 10:30
Chairperson: Roger Moser

Presentation Details

Presentation Type: Oral presentation
Title: Time-stepping methods for projection-free approximations of evolutionary geometrically constrained partial differential equations
Abstract: We consider the numerical approximation of time-dependent geometrically constrained partial differential equations. Prototypical examples are problems with sphere-valued solutions, arising, e.g., in continuum models of ferromagnetic materials (micromagnetics) or nematic liquid crystals, or problems with solutions satisfying an isometry constraint, which arise in nonlinear bending theory. For the time discretization of this class of problems, we propose a projection-free linearly implicit theta-method, which is unconditionally energy stable and, for certain choices of the parameters of the method and under a sharp discrete regularity condition, achieves second-order accuracy in the constraint violation. Furthermore, the method accommodates variable step sizes. This feature, combined with appropriate step size control strategies, allows to speed up the convergence to stationary states and to improve the accuracy of the approximations near singularities. Numerical experiments illustrate the theoretical findings and compare the proposed approach with strategies based on the linearly implicit Euler method and the two-step BDF method. This is joint work together with G. Akrivis (U Ioannina), S. Bartels (U Freiburg), and J. Wang (Harbin Institute of Technology).

Presenter

Dr Michele Ruggeri
University of Bologna | Italy

Authors

1. Ruggeri, Michele | University of Bologna