Version 1
: Received: 7 January 2020 / Approved: 9 January 2020 / Online: 9 January 2020 (07:18:53 CET)
How to cite:
Limache, A.; Aimar, H. The Continuous Galerkin Finite Element Method Is Not Naturally Consistent with the Second Law of Thermodynamics. Preprints2020, 2020010075. https://doi.org/10.20944/preprints202001.0075.v1
Limache, A.; Aimar, H. The Continuous Galerkin Finite Element Method Is Not Naturally Consistent with the Second Law of Thermodynamics. Preprints 2020, 2020010075. https://doi.org/10.20944/preprints202001.0075.v1
Limache, A.; Aimar, H. The Continuous Galerkin Finite Element Method Is Not Naturally Consistent with the Second Law of Thermodynamics. Preprints2020, 2020010075. https://doi.org/10.20944/preprints202001.0075.v1
APA Style
Limache, A., & Aimar, H. (2020). The Continuous Galerkin Finite Element Method Is Not Naturally Consistent with the Second Law of Thermodynamics. Preprints. https://doi.org/10.20944/preprints202001.0075.v1
Chicago/Turabian Style
Limache, A. and Hugo Aimar. 2020 "The Continuous Galerkin Finite Element Method Is Not Naturally Consistent with the Second Law of Thermodynamics" Preprints. https://doi.org/10.20944/preprints202001.0075.v1
Abstract
It is well known that the Continuous Galerkin Finite Element (CGFE) method is globally consistent with respect to the first law of thermodynamics. This means that, for any mesh, all obtained discrete solutions will conserve total energy. One might expect, that the method is, also, globally consistent with respect to the second law of thermodynamics. In this paper, we formally study if such conjecture is true. The heat conduction equation is used as the physical model for this analysis. In the present study it is proved that the conjecture is false: at least, for standard piecewise linear (1D and 2D) elements, the CGFE method is not always globally consistent with respect to the second law of thermodynamics. In other words, some obtained discrete solutions can violate the global postulate of the second law, which asserts that total entropy can never decrease.
Keywords
finite element method; second law of thermodynamics; heat equation; entropy
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
