Collocation methods for linear elliptic problems

COLLOCATION METHODS FOR CONTINUATION PROBLEMS IN NONLINEAR ELLIPTIC PDEs

A new class of collocation methods for nonlinear elliptic partial diierential equations is described in the context of numerical continuation studies. It is shown how the methods are well-suited for a nested dissection solution algorithm , thereby reducing computational complexity. Numerical results are given to illustrate the accuracy of the methods.

Domain Decomposition Methods for Linear-Quadratic Elliptic Optimal Control Problems

Domain Decomposition Methods for Linear-Quadratic Elliptic Optimal Control Problems

hp-Optimal discontinuous Galerkin methods for linear elliptic problems

The aim of this paper is to present and analyze a class of hpversion discontinuous Galerkin (DG) discretizations for the numerical approximation of linear elliptic problems. This class includes a number of well-known DG formulations. We will show that the methods are stable provided that the stability parameters are suitably chosen. Furthermore, on (possibly irregular) quadrilateral meshes, we ...

Comparison Between Reduced Basis and Stochastic Collocation Methods for Elliptic Problems

The stochastic collocation method [43, 1, 31, 30] has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method [28, 40, 33], primarily developed for solving parametric systems, has been recently used to deal with stochastic problems [7, 6]. In this work, we aim at comparing the performance of the two methods when applied t...

Multiscale Methods for Elliptic Problems