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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 Περβολιανάκης, Χρήστος
Thesis advisor Χατζηπαντελίδης, Παναγιώτης
Reviewer Μακριδάκης, Χαράλαμπος
Πλεξουσάκης, Μιχάλης
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].
Language Greek
Subject Finite element method
Πεπερασμένα στοιχεία
Issue date 2017-07-21
Collection   School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Post-graduate theses
  Type of Work--Post-graduate theses
Permanent Link https://elocus.lib.uoc.gr//dlib/d/d/7/metadata-dlib-1500635901-49002-10632.tkl Bookmark and Share
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