Numerical Solution of Partial Differential Equations (ΑΑ6): Διαφορά μεταξύ των αναθεωρήσεων
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* [[ | * [[Αριθμητική Επίλυση Διαφορικών Εξισώσεων με Μερικές Παραγώγους (ΑΑ6)|Ελληνική Έκδοση]] | ||
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* [https://math.uoi.gr/index.php/en/ Department of Mathematics] | * [https://math.uoi.gr/index.php/en/ Department of Mathematics] |
Αναθεώρηση της 17:40, 25 Νοεμβρίου 2022
General
School | School of Science |
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Academic Unit | Department of Mathematics |
Level of Studies | Graduate |
Course Code | AA6 |
Semester | 2 |
Course Title | Numerical Solution of Partial Differential Equations |
Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
Course Type | Special background, skills development. |
Prerequisite Courses | - |
Language of Instruction and Examinations | Greek |
Is the Course Offered to Erasmus Students | Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Upon successful completion of this course, students will be able to:
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General Competences |
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Syllabus
- Hilbert spaces, Riesz’s representation theorem, Lax-Milgram’s theorem, Cea’s theorem.
- Sobolev spaces, weak derivatives, Poincare-Friedrichs inequalities.
- Weak formulation and the Finite Element Method (FEM) for elliptic boundary value problems in 1D and 2D. A priori and a posteriori error estimates, adaptivity.
- Semi-discrete and fully-discrete schemes for parabolic equations. Temporal discretization with the Explicit and Implicit Euler methods, and the Crank-Nicolson method.
- Computer implementation of FEMs.
Teaching and Learning Methods - Evaluation
Delivery | Face-to-face. | ||||||||||||||
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Use of Information and Communications Technology |
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Teaching Methods |
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Student Performance Evaluation |
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Attached Bibliography
- “Μέθοδοι πεπερασμένων στοιχείων”, Γ. Δ. Ακρίβης, Λευκωσία, 2005.
- “Αριθμητική λύση μερικών διαφορικών εξισώσεων”, Μ. Πλεξουσάκης, & Π. Χατζηπαντελίδης, Κάλλιππος, 2015. http://hdl.handle.net/11419/665
- “The Mathematical Theory of Finite Element Methods”, S.C. Brenner, & L.R. Scott (Third ed., Vol. 15), Springer, New York, 2008.
- “Galerkin Finite Element Methods for Parabolic Problems”, V. Thomee, Springer-Verlag, 1997.