KMA/VM Variational Methods

Lecturers: Horymír Netuka
Lecture: 2 hours/week + excercise 1 hour/week
Credits: 4
Summer semester
Form of course completion: course credit, exam

• Introduction to variational methods and their great significance for applications.
• Calculus of variations: Basic definitions and statements.
• Formulation and solution of the fundamental theorem of calculus of variations.
• Variational formulations of the 2nd-order elliptic boundary problems.
• Elliptic boundary problems of the 4th-order and their variational formulations (plate bending problems).
• General elliptic problems and their solution.
• Introduction to variational inequalities: Basic theorems and some examples (plate with an obstacle, unilateral problem).
• The Ritz method for variational equations, conditions of convergence.
• The Galerkin method for variational equations, convergence.
• The Ritz-Galerkin method for solution of variational inequalities.
• Classical variational methods from computational point of view, choosing basis-functions.