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 equati...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.展开更多
基金the Natural Sciences and Engineering Research Council of Canada through the Discovery Grant program(RGPIN-05606-2015).
文摘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.
