The characteristic mixed finite element method and analysis for three-dimensional moving boundary value problem
type: Item
instance of: scholarly article
title: The characteristic mixed finite element method and analysis for three-dimensional moving boundary value problem
zbMATH Open document ID: 0859.65104
published in: Science in China. Series A
publication date: 1997-04-07T00:00:00Z
review text: Starting from the not everyday observation that ``the famous mathematician\dots and others have published famous papers on the characteristic mixed finite element method'', the author considers the problem of determining Darcy velocity, pressure and a concentration (all connected with transport of oil and gas in a porous medium) under certain boundary conditions in a parallelepiped the boundary of which moves according to a given time-dependent law. The equations for velocity and pressure contain the time only as a parameter whereas the concentration is the solution of a convection-diffusion equation. The problem is transformed to a fixed domain and rewritten into weak form as a saddle point problem combined with an evolution equation. Then a mixed finite element method for the saddle point part and a purely implicit approximation of the evolution equation are shown to converge assuming that the time step is sufficiently small (as compared to the spatial steps), that the exact solution is sufficiently smooth and the (Raviart-Thomas) elements are at least of first order.
reviewed by: Gisbert Stoyan
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 76S05
zbMATH DE Number: 908304
zbMATH Keywords: convergence
zbMATH Keywords: moving boundary value problem
zbMATH Keywords: characteristic mixed finite element method
zbMATH Keywords: transport of oil and gas
zbMATH Keywords: porous medium
zbMATH Keywords: convection-diffusion equation
zbMATH Keywords: saddle point problem
zbMATH Keywords: evolution equation
author: Yirang Yuan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 908304