An Optimal-Order Error Estimate to ELLAM Schemes for Transient Advection-Diffusion Equations on Unstructured Meshes

@article{Wang2010AnOE,
  title={An Optimal-Order Error Estimate to ELLAM Schemes for Transient Advection-Diffusion Equations on Unstructured Meshes},
  author={Kaixin Wang and Hong Wang},
  journal={SIAM J. Numer. Anal.},
  year={2010},
  volume={48},
  pages={681-707}
}
The Eulerian-Lagrangian localized adjoint method (ELLAM) provides a general characteristic procedure for solving transient advection-diffusion equations with general boundary conditions in a mass-conservative manner. In this paper we prove an optimal-order error estimate in the $L^2$ norm and a superconvergence estimate in the energy norm for the ELLAM scheme to $d$-dimensional transient advection-diffusion equations with general flux boundary conditions on unstructured meshes. 
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An Optimal-Order Error Estimate to ELLAM Schemes for Transient Advection-Diffusion Equations on Unstructured Meshes
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An optimal-order error estimate and a superconvergence estimate in the energy norm for the ELLAM scheme to d-dimensional transient advection-diffusion equations with general flux boundary conditions on unstructured meshes are proved.
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