BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Michele Ruggeri (University of Bologna) DTSTART:20260316T144000Z DTEND:20260316T161000Z DTSTAMP:20260405T175108Z UID:NSCM/211 DESCRIPTION:Title: C onvergent finite element methods for nematic liquid crystals\nby Miche le Ruggeri (University of Bologna) as part of Nečas Seminar on Continuum Mechanics\n\nLecture held in Room K3\, Faculty of Mathematics and Physics \, Charles University\, Sokolovská 83 Prague 8..\n\nAbstract\nThe Ericks en model describes nematic liquid crystals (LCs) in terms of a unit-length vector field (director) and a scalar function (degree of orientation). Co mpared to the classical Oseen-Frank model\, it allows for the description of a larger class of defects. Equilibrium states of the LC are given by ad missible pairs that minimize an energy functional\, which consists of the sum of Oseen-Frank-like energies and a double well potential. The resultin g Euler-Lagrange equations are degenerate for the director\, which poses s erious difficulties to formulate mathematically sound algorithms for their approximation. We propose a simple but novel finite element approximation of the problem that does not employ a projection to impose the unit-lengt h constraint on the director and thus circumvents the use of weakly acute meshes\,quite restrictive in 3D. We show stability and Gamma-convergence p roperties of the new method in the presence of defects. We also discuss an effective nested gradient flow algorithm for computing minimizers that co ntrols the violation of the unit-length constraint. We present several sim ulations in 2D and 3D that document the performance of the proposed scheme and its ability to capture quite intriguing defects. This is joint work w ith Ricardo H. Nochetto (University of Maryland) and Shuo Yang (BIMSA).\n LOCATION:https://researchseminars.org/talk/NSCM/211/ END:VEVENT END:VCALENDAR