Title Details: | |
Finite Elements in Higher than One-Dimension |
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Authors: |
Plexousakis, Michael Chatzipantelidis, Panagiotis |
Reviewer: |
Akrivis, George |
Subject: | MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > NUMERICAL ANALYSIS > MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > NUMERICAL ANALYSIS > |
Description: | |
Abstract: |
In this chapter we study finite element methods for elliptic problems and the heat equation in two or three spatial dimensions. We consider the variational form of the two-point elliptic problem and introduce the finite element method. We consider partitions of two-dimensional domains using triangles and show error estimations for the finite element method. We discretize the heat equation only in the spatial variables by the finite element method and thus obtain a semi-discrete problem. We show existence, uniqueness and error estimates of the solution of this semi-discrete problem. The fully discrete problem occurs by further discretizing the semi-discrete problem in time. We consider the forward Euler method, the backward Euler method and the Crank-Nicolson method. We further show stability and consistency results and derive error estimates for these methods.
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Linguistic Editors: |
Tsiadimou, Anastasia |
Technical Editors: |
Chatzipantelidis, Panagiotis |
Graphic Editors: |
Chatzipantelidis, Panagiotis |
Type: |
Chapter |
Creation Date: | 2015 |
Item Details: | |
License: |
Attribution - NonCommercial - ShareAlike 4.0 International (CC BY-NC-SA 4.0) |
Handle | http://hdl.handle.net/11419/674 |
Bibliographic Reference: | Plexousakis, M., & Chatzipantelidis, P. (2015). Finite Elements in Higher than One-Dimension [Chapter]. In Plexousakis, M., & Chatzipantelidis, P. 2015. Numerical Solution of Partial Differential Equations [Undergraduate textbook]. Kallipos, Open Academic Editions. https://hdl.handle.net/11419/674 |
Language: |
Greek |
Is Part of: |
Numerical Solution of Partial Differential Equations |
Publication Origin: |
Kallipos, Open Academic Editions |