A Compatible Embedded-Hybridized Discontinuous Galerkin Method for the Stokes-Darcy-Transport Problem  

作　　者：Aycil Cesmelioglu Sander Rhebergen 

机构地区：[1]Department ofMathematicsandStatistics,OaklandUniversity,Rochester,MI48309,USA [2]Department ofAppliedMathematics,UniversityofWaterloo,Waterloo,ONN2L3G1,Canada

出　　处：《Communications on Applied Mathematics and Computation》2022年第1期293-318,共26页应用数学与计算数学学报（英文）

基　　金：the Natural Sciences and Engineering Research Council of Canada through the Discovery Grant program(RGPIN-05606-2015).

摘　　要：We present a stability and error analysis of an embedded-hybridized discontinuous Galerkin(EDG-HDG)finite element method for coupled Stokes-Darcy flow and transport.The flow problem,governed by the Stokes-Darcy equations,is discretized by a recently introduced exactly mass conserving EDG-HDG method while an embedded discontinuous Galerkin(EDG)method is used to discretize the transport equation.We show that the coupled flow and transport discretization are compatible and stable.Furthermore,we show the existence and uniqueness of the semi-discrete transport problem and develop optimal a priori error estimates.We provide numerical examples illustrating the theoretical results.In particu-lar,we compare the compatible EDG-HDG discretization to a discretization of the coupled Stokes-Darcy and transport problem that is not compatible.We demonstrate that where the incompatible discretization may result in spurious oscillations in the solution to the trans-port problem,the compatible discretization is free of oscillations.An additional numerical example with realistic parameters is also presented.

关 键 词：Stokes-Darcyflow Coupled flowandtransport Beavers-Joseph-Saffman Embedded andhybridizedmethods Discontinuous Galerkin MULTIPHYSICS 

分 类 号：O17[理学—数学]