Finite Elements for MathMods
Additional Info
- ECTS credits: 5
- University: Leibniz University Hannover
- Semester: 2
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Topics:
The aim of this course is to provide a rigorous introduction to the mathematical foundations of the finite element method for the numerical approximation of partial differential equations. Starting from model linear elliptic boundary value problems, we develop the variational (weak) formulation within an appropriate functional analytic framework, including Sobolev spaces and fundamental results on existence and uniqueness.
The course introduces conforming finite element discretizations, with particular emphasis on the construction and characterization of finite elements and finite element spaces. Central topics include interpolation theory in Sobolev spaces, polynomial-preserving approximation operators, and their application to Lagrange and Hermite elements in multidimensional domains.
Key concepts such as consistency and convergence are studied in detail, leading to Céa-type results and a priori error estimates. Additional topics include numerical integration within the finite element framework and general considerations on convergence.
The presentation follows a mathematically rigorous approach inspired by the classical monograph of Ciarlet 1978. complemented by illustrative examples
