Чисельний аналіз на основі теорем вкладання Соболєва

Type: For the choice of university

Department: computational mathematics


SemesterAmount of hoursLecturerGroup(s)
432Associate Professor A. M. Nedashkovska


SemesterAmount of hoursGroupTeacher(s)
416Associate Professor A. M. Nedashkovska

Course description

The course “Numerical analysis based on Sobolev embedding theorems” covers the following sections: the problem of the best approximation in Banach and Hilbert spaces, generalized functions and derivatives, Lebesgue and Sobolev spaces. The main emphasis is placed on the construction of elements of the best approximation using embedding theorems for Sobolev spaces. The presentation of the material is carried out using modern terms and concepts in the field of functional analysis.

Recommended Literature

1. Михлин С.Г. Линейные уравнения в частных производных / С.Г. Михлин. – М. : Высш. школа, 1977. – 432 с.
2. Adams R. Sobolev Spaces / Robert A. Adams. – Academic Press, New York, 1975. – 268 p.
3. Dautray R. Mathematical analysis and numerical methods for science and technology. Volume 2 Functional and Variational Methods / R. Dautray, J.L. Lions. – Berlin : Springer-Verlag, 1992. – 590 p.
4. Demengel F. Sobolev Spaces and Embedding Theorems // Demengel F., Demengel G. In: Functional Spaces for the Theory of Elliptic Partial Differential Equations. Universitext. – Springer, London, 2012. – P. 57-112.
5. Hsiao G.C. Boundary Integral Equations / G.C. Hsiao, W.L. Wendland. – Berlin : Springer-Verlag, 2008. – 640 p.
6. Maz’ja V. Sobolev Spaces / V.G. Maz’ja. – Springer-Verlag, Berlin, 1985. – 488 p.
7. Steinbach O. Numerical Approximation Methods for Elliptic Boundary Value Problems / O. Steinbach. – Springer Science, 2008. – 396 p.
8. Ziemer W. Weakly Differentiable Functions, Sobolev Spaces and Functions of Bounded Variation / W.P. Ziemer. – Springer-Verlag, New York, 1989. – 308 p.


Завантажити силабус