Selected Chapters from Mathematics

Boundary value problems for ordinary differential equations of the 2nd order.
Finite difference discretization and boundary conditions.
Problems with non-smooth soefficients and/or right hand side.
Variational formulation of the boundary value problems.
Discretization based on variational formulation. Collocation, Ritz method, Galerkin method, finite element method.
Propertis and direct methods of solution of the discretized systems.
Conjugate gradient method with preconditioning.
Domain decomposition and multilevel methods.
Variational inequalities and their discretization.
Numerical solution of variational inequalities.
Boundary integral equations.
Bouhary element method for a model problem.
Software.