An immersed Eulerian-Lagrangian localized adjoint method for transient advection-diffusion equations with interfaces
K. Wang 1, H. Wang 2, X. Yu 31 School of Mathematics, Shandong University, Jinan, Shandong 250100, China
2 Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208, USA
3 Laboratory of Applied Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
Received by the editors February 16, 2010 and, in revised form, October 18, 2010.
We develop and analyze an immersed Eulerian-Lagrangian localized adjoint method (ImELLAM) for transient advection-diffusion equations with interfaces. The derived method possesses the combined advantages of the immersed finite element method and the Eulerian-Lagrangian method.AMS subject classifications: 65N15, 65N30, 65M60
Key words: Advection-diffusion problem, Eulerian-Lagrangian method, error estimate, immersed finite element method, interfaces.