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- W2965702953 abstract "Abstract We consider a system of second-order nonlinear elliptic partial differential equations that models the equilibrium configurations of a two-dimensional planar bistable nematic liquid crystal device. Discontinuous Galerkin (dG) finite element methods are used to approximate the solutions of this nonlinear problem with nonhomogeneous Dirichlet boundary conditions. A discrete inf–sup condition demonstrates the stability of the dG discretization of a well-posed linear problem. We then establish the existence and local uniqueness of the discrete solution of the nonlinear problem. A priori error estimates in the energy and $mathbf{L}^2$ norms are derived and a best approximation property is demonstrated. Further, we prove the quadratic convergence of the Newton iterates along with complementary numerical experiments." @default.
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- W2965702953 date "2020-06-19" @default.
- W2965702953 modified "2023-09-23" @default.
- W2965702953 title "Discontinuous Galerkin finite element methods for the Landau–de Gennes minimization problem of liquid crystals" @default.
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- W2965702953 doi "https://doi.org/10.1093/imanum/draa008" @default.
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