Course Details

The basic goal of the course is the presentation of the finite element method in a general framework that enables dealing with a big variety of problems in mechanics. The basic target is utilizing the method and it is met by emphasizing on its computational implementation.

On realistic modeling of physico-chemical phenomena. On approximate solution methods of partial differential equations governing the conservation of mass, energy and momentum.

Introduction to the discretization methods of conservation equations. Introduction to the finite element method. Galerkin weighted residuals. The Galerkin/finite element method. Variational formulation – Rayleigh-Ritz method. Elements of mesh generation. Basis functions in one-dimensional and two-dimensional domains. Error estimates.

Isoparametric mapping. Standard basis functions. Numerical integration.

Discretization of one-dimensional, linear, boundary value problems – matrix assembly. Discretization of two-dimensional, linear, boundary value problems – matrix assembly. Accommodation of Dirichlet, Neumann and Robin boundary conditions. Code development.

Direct matrix solvers. Sparse matrix solvers. Implementation of the frontal solver.

Discretization of one- and two- dimensional nonlinear boundary value problems. Newton iteration. Parameter continuation. On the analysis of solution multiplicity and stability.

Computational laboratory – development of finite element fortran source codes. Introduction to the commercial code Comsol Mupltiphysics.