Abstract
This paper illustrates the use of an adaptive finite element method to solve a nonlinear singularly perturbed boundary value problem which arises from a one-dimensional Q-tensor model of liquid crystals. The adaptive non-uniform mesh is generated by equidistribution of a strictly positive monitor function which is a linear combination of a constant floor and a power of the first derivative of the numerical solution. By an appropriate selection of the monitor function parameters, we show that the computed numerical solution converges at an optimal rate with respect to the mesh density and that the solution accuracy is robust to the size of the singular perturbation parameter. (C) 2012 Elsevier Ltd. All rights reserved.