Course for international guest/part time students
- Faculty
- Faculty of Science
- Organization
- TTK Department of Applied Analysis and Computational Mathematics
- Code
- elpdnm1u0um17gm
- Title
- Numerical solution of elliptic partial differential equations 1. (p)
- Usual semester
- Autumn
- Published semester
- 2026/27/1
- ECTS
- 3
- Language
- hu
- Learning outcomes
- Knowledge: getting familiar with the modern notions of numerical methods for elliptic partial differential equations Ability: to understand and use numerical methods for elliptic partial differential equations Attitude: the need to deepen the applied mathematical knowledge, to gain new applied mathematical skills, to develop competencies. The aim to apply the mathematical knowledge for a wide range of problems Autonomy: based on the gained knowledge in the numerical methods for elliptic partial differential equations, the students are able to decide which tools are the most suitable to solve applied problems Responsibility: the importance of the precise formulation of mathematical thinking and notions is clear to the students, who are at the same time aware of the applicability and the boundaries of numerical methods for elliptic partial differential equations
- Course content
- Background for linear elliptic boundary value problems. Finite difference methods. Construction, stability and convergence. Iterative solution methods, preconditioning. Multigrid. Finite element methods. Variational formulation, basis functions, convergence. Qualitative properties, discrete maximum principles. A posteriori error estimation. Nonlinear elliptic boundary value problems, Newton type methods. Necessary prior knowledge: numerical methods for ordinary differential equations, linear elliptic boundary value problems
- Assessment method
- exam grade, practical grade (5-point scale)
- Bibliography
- lecture notes
- Recommended bibliography
- - Karátson J.: Numerical methods for elliptic partial differential equations, lecture notes - Süli, E., Lecture Notes on Finite Element Method for Partial Differential Equations, Mathematical Institute, University of Oxford, 2012 - Faragó I., Karátson J.: Numerical solution of nonlinear elliptic problems via preconditioning operators: theory and applications. Nova Science, 2002