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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)
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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)
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Oral exam. Last update: Vejchodský Tomáš, doc. RNDr., Ph.D. (07.06.2019)
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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)
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Oral examination from topics discussed during the course Last update: Vlasák Miloslav, RNDr., Ph.D. (26.02.2018)
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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)
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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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