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Method of asymptotic partial decomposition with discontinuous junctions
- Source :
- Computers & Mathematics with Applications. 105:75-93
- Publication Year :
- 2022
- Publisher :
- Elsevier BV, 2022.
-
Abstract
- Method of asymptotic partial decomposition of a domain (MAPDD) proposed and justified earlier for thin domains (rod structures, tube structures consisting of a set of thin cylinders) generates some specific interface conditions between three-dimensional and one-dimensional parts. In the case of the heat equation these conditions ensure the continuity of the solution and continuity in average of the normal flux. However for some computational reasons the strong continuity condition for the solution may be undesirable. It may be preferable to replace it by more flexible condition of continuity in average over the interface cross section. In the present paper we introduce and justify this alternative junction condition allowing such discontinuity of the solution of both stationary and non-stationary problems. The closeness of solutions of these hybrid dimension problems to the solution of the fully three-dimensional setting is proved. At the discrete level, finite volume schemes are considered, an error estimate is established. The new version of the MAPDD is compared to the classical one via numerical tests. It shows better stability of the new scheme.
- Subjects :
- AMS classification: 35B27, 35Q53, 35C20, 35J25, 65N12, 76M12
asymptotic expansion
Finite volume method
heat equation
dimension reduction
Mathematical analysis
010103 numerical & computational mathematics
method of asymptotic partial decomposition of the domain
01 natural sciences
Stability (probability)
010101 applied mathematics
Set (abstract data type)
Computational Mathematics
Discontinuity (linguistics)
Cross section (physics)
Computational Theory and Mathematics
Dimension (vector space)
Modeling and Simulation
interface
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Heat equation
[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]
0101 mathematics
Asymptotic expansion
Mathematics
Subjects
Details
- ISSN :
- 08981221
- Volume :
- 105
- Database :
- OpenAIRE
- Journal :
- Computers & Mathematics with Applications
- Accession number :
- edsair.doi.dedup.....462ea0b2460823db853513c8c4dc4938