Post-graduate theses
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Identifier |
000410116 |
Title |
Εκ των υστέρων εκτιμήσεις σφάλματος για ελλειπτικές εξισώσεις |
Alternative Title |
A posteriori error estimation for elliptic equations |
Author
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Περβολιανάκης, Χρήστος
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Thesis advisor
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Χατζηπαντελίδης, Παναγιώτης
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Reviewer
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Μακριδάκης, Χαράλαμπος
Πλεξουσάκης, Μιχάλης
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Abstract |
When using the finite element method, in the applications, there may be specific areas
in the domain where the numerical approximation is poor. A natural choice, to tackle this
problem, is to refine the discretisation in the elements where the error contribution is
relative large. However, the following question arises. How can these areas be defined?
An answer to the question is to develop local estimators for the error of the finite
element method in each element to indicate the magnitude of the local error. A priori
error estimates known from the finite element method, are not practical, as they generally
depend on the unknown solution of the problem, but they help in the theoretical determination
of the error convergence rate. It is possible to construct a posteriori error estimators, which
will be measurable and depend on the finite element solution and problem’s data.
The a posteriori error estimators are a very useful tool for the finite element method,
once they check the total error and at the same time give information about the distribution
of the error in the individual elements.
A key attribute of an a posteriori error estimator is that it should have little computational
cost compared to solving the overall problem. Therefore, the estimators should either be
solved directly by the problem data and the finite element solution, or by solving small
auxiliary problems in some suitable subdomains.
In this thesis we will have an extensive presentation of the frequent a posteriori estimators
for the finite element method, based on the book A posteriori Error Estimation in Finite
Element Analysis by M.Ainsworth, JTOden [2] and on the book A Review of A Posteriori
Error Estimation and Adaptive Mesh-Refinement Techniques by R.Verfürth [15].
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Language |
Greek |
Subject |
Finite element method |
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Πεπερασμένα στοιχεία |
Issue date |
2017-07-21 |
Collection
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School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Post-graduate theses
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Type of Work--Post-graduate theses
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Permanent Link |
https://elocus.lib.uoc.gr//dlib/d/d/7/metadata-dlib-1500635901-49002-10632.tkl
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