Title Details: | |
Heat Equation: Finite Elements |
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Authors: |
Plexousakis, Michail Chatzipantelidis, Panagiotis |
Reviewer: |
Akrivis, George |
Subject: | MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > NUMERICAL ANALYSIS > |
Description: | |
Abstract: |
In this chapter we study finite element methods for simple parabolic equations in one spatial and one time variable. We introduce the concept of the semi-discrete problem, i.e. the discretization only with respect to the spatial variable. We show existence and uniqueness of the solution of the semi-discrete problem.
We obtain the fully discrete problem by discretizing the semi-discrete problem also 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/11419/672 |
Bibliographic Reference: | Plexousakis, M., & Chatzipantelidis, P. (2015). Heat Equation: Finite Elements [Chapter]. In Plexousakis, M., & Chatzipantelidis, P. 2015. Numerical Solution of Partial Differential Equations [Undergraduate textbook]. Kallipos, Open Academic Editions. https://hdl.handle.net/11419/672 |
Language: |
Greek |
Is Part of: |
Numerical Solution of Partial Differential Equations |
Publication Origin: |
Kallipos, Open Academic Editions |