Convergence of the finite volume method for a conductive-radiative heat transfer problem
We show that the finite volume method rigorously converges to the solution of a conductive-radiative heat transfer problem with nonlocal and nonlinear boundary conditions. To get this result, we start by proving existence of solutions for a finite volume discretization of the original problem. Then,...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Vilnius Gediminas Technical University
2013-04-01
|
| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/4113 |
| _version_ | 1818893457903583232 |
|---|---|
| author | Karlis Birgelis Uldis Raitums |
| author_facet | Karlis Birgelis Uldis Raitums |
| author_sort | Karlis Birgelis |
| collection | DOAJ |
| description | We show that the finite volume method rigorously converges to the solution of a conductive-radiative heat transfer problem with nonlocal and nonlinear boundary conditions. To get this result, we start by proving existence of solutions for a finite volume discretization of the original problem. Then, by obtaining uniform boundedness of discrete solutions and their discrete gradients with respect to mesh size, we finally get L 2type convergence of discrete solutions. |
| first_indexed | 2024-12-19T18:12:55Z |
| format | Article |
| id | doaj.art-ee002079d5864ce0bad0a136cedb156a |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-19T18:12:55Z |
| publishDate | 2013-04-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-ee002079d5864ce0bad0a136cedb156a2022-12-21T20:11:15ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102013-04-0118210.3846/13926292.2013.783885Convergence of the finite volume method for a conductive-radiative heat transfer problemKarlis Birgelis0Uldis Raitums1Faculty of Physics and Mathematics, University of Latvia Zellu st. 8, LV-1002 Riga, LatviaFaculty of Physics and Mathematics, University of Latvia Zellu st. 8, LV-1002 Riga, LatviaWe show that the finite volume method rigorously converges to the solution of a conductive-radiative heat transfer problem with nonlocal and nonlinear boundary conditions. To get this result, we start by proving existence of solutions for a finite volume discretization of the original problem. Then, by obtaining uniform boundedness of discrete solutions and their discrete gradients with respect to mesh size, we finally get L 2type convergence of discrete solutions.https://journals.vgtu.lt/index.php/MMA/article/view/4113conductive-radiative heat transferfinite volume methodnonlocal and nonlinear boundary conditionsconvergence |
| spellingShingle | Karlis Birgelis Uldis Raitums Convergence of the finite volume method for a conductive-radiative heat transfer problem Mathematical Modelling and Analysis conductive-radiative heat transfer finite volume method nonlocal and nonlinear boundary conditions convergence |
| title | Convergence of the finite volume method for a conductive-radiative heat transfer problem |
| title_full | Convergence of the finite volume method for a conductive-radiative heat transfer problem |
| title_fullStr | Convergence of the finite volume method for a conductive-radiative heat transfer problem |
| title_full_unstemmed | Convergence of the finite volume method for a conductive-radiative heat transfer problem |
| title_short | Convergence of the finite volume method for a conductive-radiative heat transfer problem |
| title_sort | convergence of the finite volume method for a conductive radiative heat transfer problem |
| topic | conductive-radiative heat transfer finite volume method nonlocal and nonlinear boundary conditions convergence |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/4113 |
| work_keys_str_mv | AT karlisbirgelis convergenceofthefinitevolumemethodforaconductiveradiativeheattransferproblem AT uldisraitums convergenceofthefinitevolumemethodforaconductiveradiativeheattransferproblem |