1.       

Course title

Computer algebra. Finite element method

2.       

Year of study, study programme

4,

1-31 03 09 Computer Mathematics and Systems Analysis

3.       

Semester of study

7

4.       

Number of credits

2

5.       

Lecturer

Lavrova Olga Anatolievna

6.       

Course Objective

Formation of theoretical knowledge and practical skills for solving problems of mathematical physics by means of finite element method.

As a result of studying the student should be able to

–         construct variational and discrete formulations for elliptic boundary value problems of the second order;

–         analyze existence and uniqueness of solutions for variational problems in Sobolev spaces;

–         solve the problems of mathematical physics by the finite element method.

7.       

Prerequisites

Algebra and Number Theory. Computer Mathematics. Equations of Mathematical Physics. Numerical Methods

8.       

Course content

1.  Types of partial differential equations of the second order. Variational formulation of the boundary-value problem. Sobolev spaces. Existence and uniqueness of weak solutions.

2.  Galerkin method. Finite element. Finite element spaces. Element-wise construction of the discrete problem.

3.  Convergence of the finite element method. Approximation theorems. A-priori error estimates. A-posteriori error estimates.

4.  The finite element method in system of computer mathematics (MATLAВ, Mathematica) and programming languages (FEniCS-project).

9.       

Recommended Literature

1.     Ciarlet P. The finite element method for elliptic problems. North-Holland Publishing Company, 1978.

2.     Оганесян Л.А., Руховец Л.А. Вариационно-разностные методы решения эллиптических уравнений. Ереван: Изд-во АН АрмССР, 1979.

3.     Шайдуров В.В. Многосеточные методы конечных элементов. М.: Наука, 1989.

4.     H. Goering, H-S. Roos, L. Tobiska, Finite-Elementе-Methode für Anfänger, 4. Auflage, Wiley-VCH, Berlin, 2010.

5.     Голубева, Л. Л. Компьютерная математика. Числовой пакет MATLAB: курс лекций / Л. Л. Голубева, А. Э. Малевич, Н. Л. Щеглова. Минск: БГУ, 2007. 164 с.

6.     Голубева, Л. Л. Компьютерная математика. Числовой пакет MATLAB: лабораторный практикум / Л. Л. Голубева, А. Э. Малевич, Н. Л. Щеглова. Минск: БГУ, 2008. 171 с.

7.     Голубева, Л. Л. Компьютерная математика. Символьный пакет Mathematica: лаб. практикум. В 2 ч. Ч 1. / Л. Л. Голубева, А. Э. Малевич, Н. Л. Щеглова. Минск: БГУ, 2012. 235 с. http://elib.bsu.by/handle/123456789/95686

8.     Langtangen, H.P., Logg, A. Solving PDEs in Python – The FEniCS Tutorial Volume I. Berlin, Springer, 2016.

10.   

Teaching Methods

Lectures, laboratory classes

11.   

Teaching language

Russian

12.   

Requirements, current control

Control of the student’s work takes place in the form of tests and interviews (reports) on laboratory works with their oral defense. Credits are held either orally or in writing.

13.   

Method of certification

Credit