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Course, academic year 2024/2025
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Techniques for a posteriori error estimation - NMNV461
Title: Techniky aposteriorního odhadování chyby
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: doc. RNDr. Tomáš Vejchodský, Ph.D.
Teacher(s): doc. RNDr. Tomáš Vejchodský, Ph.D.
Class: M Mgr. NVM
M Mgr. NVM > Volitelné
Classification: Mathematics > Numerical Analysis
Incompatibility : NMOD023
Interchangeability : NMOD023
Is interchangeable with: NMOD023
Annotation -
Numerical solutions should always be accompanied by a posteriori error estimates. Besides the qualitative information about the error, they enable to find the spatial distribution of the error and optimize the computation by adaptive techniques. The course provides an overview of techniques for a posteriori error estimates and compares their properties.
Last update: T_KNM (13.04.2015)
Aim of the course -

Students will get an overview about the techniques of the a posteriori error estimation for the elliptic and parabolic partial differential equations.

Last update: T_KNM (07.04.2015)
Course completion requirements -

Oral exam.

Last update: Vejchodský Tomáš, doc. RNDr., Ph.D. (07.06.2019)
Literature - Czech

Ainsworth, M.; Oden, J.T.: A posteriori error estimation in finite element analysis. Wiley, New York, 2000.

Bangerth, W.; Rannacher, R.: Adaptive finite element methods for differential equations. Birkhäuser Verlag, Basel, 2003.

Verfürth, R.: A posteriori error estimation techniques for finite element methods. Oxford University Press, Oxford, 2013.

Last update: T_KNM (07.04.2015)
Requirements to the exam -

Oral examination from topics discussed during the course

Last update: Vlasák Miloslav, RNDr., Ph.D. (26.02.2018)
Syllabus -

Numerical solution can hardly be reliable if we do not know how inaccurate it is. A posteriori error estimates provide the information about the size of the error and therefore they should supplement all numerical solutions. Besides this, the a posteriori error estimates enable to find the spatial distribution of the error among the computational domain and optimize the computation by adaptive techniques. This course offers an overview of techniques for a posteriori error estimation. In particular, it covers explicit and implicit residual estimates, hierarchical estimates, estimates based on the postprocessing and goal oriented estimates. (The complementary estimates are covered by the course A posteriori numerical analysis by the equilibrated fluxes.) Based on the example of Poisson equation discretized by the finite element method, we will explain individual techniques and prove their properties.

Last update: Kučera Václav, doc. RNDr., Ph.D. (15.01.2019)
Entry requirements -

Linear elliptic partial differential equations of second order, weak formulation, Laplace operator, basics of the finite element method. Lectures will be adapted to respect the background of students.

Last update: Vejchodský Tomáš, doc. RNDr., Ph.D. (02.05.2018)
 
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