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Full-Text Articles in Physical Sciences and Mathematics
The Averaging Lemma, Ronald A. Devore, Guergana Petrova
The Averaging Lemma, Ronald A. Devore, Guergana Petrova
Faculty Publications
No abstract provided.
An Approximation To Miscible Fluid Flows In Porous Media With Point Sources And Sinks By An Eulerian-Lagrangian Localized Adjoint Method And Mixed Finite Element Methods, Hong Wang, Liang Dong, Richard E. Ewing, Stephen L. Lyons, Guan Qin
An Approximation To Miscible Fluid Flows In Porous Media With Point Sources And Sinks By An Eulerian-Lagrangian Localized Adjoint Method And Mixed Finite Element Methods, Hong Wang, Liang Dong, Richard E. Ewing, Stephen L. Lyons, Guan Qin
Faculty Publications
We develop an Eulerian–Lagrangian localized adjoint method (ELLAM)-mixed finite element method (MFEM) solution technique for accurate numerical simulation of coupled systems of partial differential equations (PDEs), which describe complex fluid flow processes in porous media. An ELLAM, which was shown previously to outperform many widely used methods in the context of linear convection-diffusion PDEs, is presented to solve the transport equation for concentration. Since accurate fluid velocities are crucial in numerical simulations, an MFEM is used to solve the pressure equation for the pressure and Darcy velocity. This minimizes the numerical difficulties occurring in standard methods for approximating velocities caused …
An Optimal-Order Error Estimate For An Ellam Scheme For Two-Dimensional Linear Advection-Diffusion Equations, Hong Wang
Faculty Publications
An Eulerian-Lagrangian localized adjoint method (ELLAM) is presented and an- alyzed for two-dimensional linear advection-diffusion partial differential equations (PDEs). An optimal-order error estimate in the L^2 norm and a superconvergence estimate in a discrete H^1 norm are derived. Numerical experiments are performed to verify the theoretical estimates.