| Abstract: |
| The finite volume method (FVM) is well-known as the numerical techniques for partial differential equations. Particularly, since the conservation law is guaranteed locally, it is widely employed for physic-based problems. In this talk, we apply FVM to the analysis for the moisture transport in the one-dimensional porous materials. The transport process is given as the quasi-linear partial differential equations of parabolic type with non-monotone boundary conditions, which poses significant mathematical challenges for establishing the existence of strong solutions, as the standard evolution equation theory is not directly applicable. To overcome these difficulties, we succeed in showing strong solvability by employing FVM. Moreover, we derive error estimates for the approximate solutions. The aims of this talk are to explain our approach and to highlight the theoretical and numerical advantages of the finite volume method for quasilinear parabolic equations accompanying the non-monotone boundary conditions. |
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