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
TLDR
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.

References

SHOWING 1-10 OF 11 REFERENCES
An Optimal-Order Error Estimate for a Family of ELLAM-MFEM Approximations to Porous Medium Flow
TLDR
An optimal-order error estimate is proved for a family of ELLAM-MFEM approximations, which simulates porous medium flow accurately even if large spatial grids and time steps are used.
An optimal-order L2-error estimate for nonsymmetric discontinuous Galerkin methods for a parabolic equation in multiple space dimensions
A fast characteristic finite difference method for fractional advection–diffusion equations
An Eulerian-Lagrangian Formulation For Compositional Flow In Porous Media
We derive an Eulerian-Lagrangian formulation for two-phase, multicomponent compositional flow in porous media with sources and sinks. The formulation can be used by many Eulerian-Lagrangian methods…
A Fast Finite Difference Method for Two-Dimensional Space-Fractional Diffusion Equations
TLDR
A fast and yet accurate solution method for the implicit finite difference discretization of space-fractional diffusion equations in two space dimensions by carefully analyzing the structure of the coefficient matrices is developed.
A direct O(N log2 N) finite difference method for fractional diffusion equations
A fast Galerkin method with efficient matrix assembly and storage for a peridynamic model
An Optimal-Order Error Estimate to ELLAM Schemes for Transient Advection-Diffusion Equations on Unstructured Meshes
TLDR
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.
@BULLET Numerical Methods for Partial Differential Equations, 2000-present @BULLET Journal of Korean SIAM, 2001–present @BULLET Computing and Visualization in Science
  • –present @BULLET The Modeling and Computation for Flow and Transport
  • 2004
An O(N log 2 N ) alternating-direction finite difference method for two-dimensional fractional diffusion equations
  • J. Comput. Phys
  • 2011
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