Analysis of a DG–XFEM Discretization for a Class of Two–Phase Mass Transport Problems
نویسندگان
چکیده
We consider a standard model for mass transport across an evolving interface. The solution has to satisfy a jump condition across an evolving interface. We present and analyze a finite element discretization method for this mass transport problem. This method is based on a space-time approach in which a discontinuous Galerkin (DG) technique is combined with an extended finite element method (XFEM). The jump condition is satisfied in a weak sense by using the Nitsche method. This Nitsche DG-XFEM method is new. An error analysis is presented which results in optimal discretization error bounds. Results of numerical experiments are given which illustrate the accuracy of the method. AMS subject classification. 65N12, 65N30
منابع مشابه
Analysis of a Nitsche XFEM-DG Discretization for a Class of Two-Phase Mass Transport Problems
We consider a standard model for mass transport across an evolving interface. The solution has to satisfy a jump condition across an evolving interface. We present and analyze a finite element discretization method for this mass transport problem. This method is based on a space-time approach in which a discontinuous Galerkin (DG) technique is combined with an extended finite element method (XF...
متن کاملNitsche-XFEM with Streamline Diffusion Stabilization for a Two-Phase Mass Transport Problem
We consider an unsteady convection diffusion equation which models the transport of a dissolved species in two-phase incompressible flow problems. The so-called Henry interface condition leads to a jump condition for the concentration at the interface between the two phases. In [A. Hansbo, P. Hansbo, Comput. Methods Appl. Mech. Engrg. 191 (20002)], for the purely elliptic stationary case, exten...
متن کاملThe Nitsche XFEM-DG space-time method and its implementation in three space dimensions
We consider a standard model for mass transport across an evolving interface. The solution has to satisfy a jump condition across an evolving interface. In the recent paper [C. Lehrenfeld, A. Reusken, SIAM J. Num. Anal., 51 (2013)] a new finite element discretization method for this mass transport problem is presented and analyzed. This method is based on a space-time approach in which a discon...
متن کاملFinite Element Techniques for the Numerical Simulation of Two-Phase Flows with Mass Transport
We consider a standard sharp interface model for the fluid dynamics in a twophase incompressible flow, combined with a convection-diffusion model for solute transport. Some important numerical challenges related to these models are discussed. We present a finite element discretization method for the solute transport model. The method is based on an Eulerian approach, i.e. computational grids ar...
متن کاملAnalysis of an Extended Pressure Finite Element Space for Two-phase Incompressible Flows
We consider a standard model for incompressible two-phase flows in which a localized force at the interface describes the effect of surface tension. If a level set (or VOF) method is applied then the interface, which is implicitly given by the zero level of the level set function, is in general not aligned with the triangulation that is used in the discretization of the flow problem. This nonal...
متن کامل