A mimetic finite difference method using Crank-Nicolson scheme for unsteady diffusion equation
n this article a new mimetic finite difference method to solve unsteady diffusion equation is presented. It uses Crank-Nicolson scheme to obtain time approximations and second order mimetic discretizations for gradient and divergence operators in space. The convergence of this new method is analyzed...
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| Format: | Article |
| Language: | English |
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Universidad de Costa Rica
2010-04-01
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| Series: | Revista de Matemática: Teoría y Aplicaciones |
| Online Access: | https://revistas.ucr.ac.cr/index.php/matematica/article/view/302 |
| _version_ | 1797716106586095616 |
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| author | Iliana A. Mannarino |
| author_facet | Iliana A. Mannarino |
| author_sort | Iliana A. Mannarino |
| collection | DOAJ |
| description | n this article a new mimetic finite difference method to solve unsteady diffusion
equation is presented. It uses Crank-Nicolson scheme to obtain time approximations
and second order mimetic discretizations for gradient and divergence operators in
space. The convergence of this new method is analyzed using Lax-Friedrichs equiv-
alence theorem. This analysis is developed for one dimensional case. In addition to
the analytical work, we provide experimental evidences that mimetic Crank-Nicolson
scheme is better than standard finite difference because it achieves quadratic conver-
gence rates, second order truncation errors and better approximations to the exact
solution.
Keywords: mimetic scheme, finite difference method, unsteady diffusion equation,
Lax-Friedrichs equivalence theorem. |
| first_indexed | 2024-03-12T08:16:36Z |
| format | Article |
| id | doaj.art-32000fa4f9d14e9894dec56f019f0fe8 |
| institution | Directory Open Access Journal |
| issn | 2215-3373 |
| language | English |
| last_indexed | 2024-03-12T08:16:36Z |
| publishDate | 2010-04-01 |
| publisher | Universidad de Costa Rica |
| record_format | Article |
| series | Revista de Matemática: Teoría y Aplicaciones |
| spelling | doaj.art-32000fa4f9d14e9894dec56f019f0fe82023-09-02T18:45:59ZengUniversidad de Costa RicaRevista de Matemática: Teoría y Aplicaciones2215-33732010-04-0116222123010.15517/rmta.v16i2.302287A mimetic finite difference method using Crank-Nicolson scheme for unsteady diffusion equationIliana A. Mannarino0Universidad Central de Venezuela, Facultad de Ciencias, Escuela de Matemáticasn this article a new mimetic finite difference method to solve unsteady diffusion equation is presented. It uses Crank-Nicolson scheme to obtain time approximations and second order mimetic discretizations for gradient and divergence operators in space. The convergence of this new method is analyzed using Lax-Friedrichs equiv- alence theorem. This analysis is developed for one dimensional case. In addition to the analytical work, we provide experimental evidences that mimetic Crank-Nicolson scheme is better than standard finite difference because it achieves quadratic conver- gence rates, second order truncation errors and better approximations to the exact solution. Keywords: mimetic scheme, finite difference method, unsteady diffusion equation, Lax-Friedrichs equivalence theorem.https://revistas.ucr.ac.cr/index.php/matematica/article/view/302 |
| spellingShingle | Iliana A. Mannarino A mimetic finite difference method using Crank-Nicolson scheme for unsteady diffusion equation Revista de Matemática: Teoría y Aplicaciones |
| title | A mimetic finite difference method using Crank-Nicolson scheme for unsteady diffusion equation |
| title_full | A mimetic finite difference method using Crank-Nicolson scheme for unsteady diffusion equation |
| title_fullStr | A mimetic finite difference method using Crank-Nicolson scheme for unsteady diffusion equation |
| title_full_unstemmed | A mimetic finite difference method using Crank-Nicolson scheme for unsteady diffusion equation |
| title_short | A mimetic finite difference method using Crank-Nicolson scheme for unsteady diffusion equation |
| title_sort | mimetic finite difference method using crank nicolson scheme for unsteady diffusion equation |
| url | https://revistas.ucr.ac.cr/index.php/matematica/article/view/302 |
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