A uniformly optimal-order error estimate of an ELLAM scheme for unsteady-state advection-diffusion equations
Kaixin Wang 11 School of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, China
Received by the editors March 31, 2007
We prove an optimal-order error estimate in a weighted energy norm for the Eulerian-Lagrangian localized adjoint method (ELLAM) for unsteadystate advection-diffusion equations with general inflow and outflow boundary conditions. It is well known that these problems admit dynamic fronts with interior and boundary layers. The estimate holds uniformly with respect to the vanishing diffusion coefficient.
AMS subject classifications: 35R35, 49J40, 60G40
Key words: characteristic methods; Eulerian-Lagrangian methods; interpolation of spaces; uniform error estimates