Zeitschriftenartikel:
R. Nochetto, M. Ruggeri, S. Yang:
"Gamma-convergent projection-free finite element methods for nematic liquid crystals: The Ericksen model";
SIAM Journal on Numerical Analysis,
60
(2022),
2;
S. 856
- 887.
Kurzfassung englisch:
The Ericksen model for nematic liquid crystals couples a director field with a scalar degree of orientation variable and allows the formation of various defects with finite energy. We propose a simple but novel finite element approximation of the problem that can be implemented easily within standard finite element packages. Our scheme is projection-free and thus circumvents the use of weakly acute meshes, which are quite restrictive in three dimensions but are required by recent algorithms for convergence. We prove stability and Γ-convergence properties of the new method in the presence of defects. We also design an effective nested gradient flow algorithm for computing minimizers that controls the violation of the unit-length constraint of the director. We present several simulations in two and three dimensions that document the performance of the proposed scheme and its ability to capture quite intriguing defects.
"Offizielle" elektronische Version der Publikation (entsprechend ihrem Digital Object Identifier - DOI)
http://dx.doi.org/10.1137/21M1407495