| Abstract: | A number of numerical methods for mildly nonlinear elliptic boundary value problems on general domains is presented. The discretization procedures considered are: a fourth-order FFT-type method, collocation using Hermite bicubic splines and Galerkin with linear triangular as well as quadratic quadrilateral isoparametric elements. The linearized collocation and Galerkin equations are solved by various direct methods available in the ELLPACK system. A comparative study of the above equation solvers is presented for different domain geometries and compilers. The evaluation of software for the general mildly nonlinear elliptic equations is performed over 36 instances from a population of 16 parametrized problems with ‘real world’ and ‘mathematical’ behaviour. The performance data suggests that collocation is an effective method for such general problems, while Galerkin with quadratic quadrilateral isoparametric elements is uniformly superior to the one with linear elements. |
