Abstract
We study higher order MUSCL type finite volume scheme applied to linear convection dominated diffusion problem in a bounded convex domain Ω ⊂ ℝ2. Although the original problem is linear, the numerical problem becomes non-linear, due to MUSCL type reconstruction/limiter technique. For second order schemes, an a-priori estimate of order h2 for the discrete L2 norm is obtained. Moreover, we discuss the solvability of the corresponding nonlinear discrete problem.
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