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

Authors:
Kaixin Wang;Hong Wang
Affiliations:
kx.wang@mail.sdu.edu.cn;hwang@math.sc.edu
Venue:
SIAM Journal on Numerical Analysis
Year:
2010

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Abstract

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.