470-4502/01 – Numerical Methods II (NM2)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantorprof. RNDr. Radim Blaheta, CSc.Subject version guarantorprof. RNDr. Radim Blaheta, CSc.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
BLA19 prof. RNDr. Radim Blaheta, CSc.
DOM0015 Ing. Simona Domesová
LUK76 doc. Ing. Dalibor Lukáš, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 10+10

Subject aims expressed by acquired skills and competences

The course will introduce students to the basic principles of formulation of boundary and initial value problems and mathematical derivation of the finite element method. An attention is also paid to the computer implementation and analysis of the accuracy of the method. Theoretical foundations provide qualified assessment of the results obtained by the available software tools as well as a further development of the finite element methods.

Teaching methods

Lectures
Tutorials

Summary

The course deals with a description of the finite element method and its use for solving boundary and initial value problems arising in mathematical modeling of physical processes, such as problems of heat conduction, elasticity etc.

Compulsory literature:

K. Rektorys:. Variational Methods in Mathematics, Science and Engineering, D. Reidel Publ. Comp, NY 1975

Recommended literature:

C. Johnson: Numerical solution of partial differential equations by the finite element method, Cambridge Univ. Press, 1995

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

There are not defined other requirements for student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: Mathematical formulations of boundary and initial value problems describing physical phenomena. Advantages of mathematical modeling and correct use of mathematical models. Mathematical formulations of 2D and 3D problems. Variational (weak) formulations. Energy functional and formulations. Existence and regularity of solutions. Ritz-Galerkin method. Finite element method in 1D. Finite element method in 2D and 3D. Programming of FEM. Reference element. Isoparameteric finite elements. FEM error. Apriori estimates. Aposteriori estimates. Adaptive methods, optimal grids. Nonconform and mixed methods. Nonlinear problems. Tutorials: Derivation of mathematical formulations of boundary and initial value problems for various physical phenomena. Variational (weak) formulations. Use of Ritz-Galerkin method. FEM algorithm. Programming, pre and postprocessing. Solution to selected problems, discretization error. Use of commercial software. Projects: Projects consist of a series of simple problems, the solution to which makes use of the theory. Projects may be concerned with programming of FEM.

Conditions for subject completion

Full-time form (validity from: 2011/2012 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 30  15
        Examination Examination 70  21
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava 1 Compulsory study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC P Czech Ostrava 1 Compulsory study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava 1 Compulsory study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC K Czech Ostrava 1 Compulsory study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2014/2015 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2014/2015 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2013/2014 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2013/2014 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2012/2013 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2012/2013 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2011/2012 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2011/2012 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2010/2011 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2010/2011 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner