On the Uniform Convergence of the Scharfetter–Gummel Discretization in One Dimension

DOI10.1137/0730037zbMath0790.65082OpenAlexW2018305879MaRDI QIDQ4202394

Eugene C. Gartland jun.

Publication date: 23 June 1994

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0730037

zbMATH Keywords

monotonicityerror estimatesconsistencyuniform convergenceviscosity solutionScharfetter-Gummel scheme

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (6)

Viscous Equations Treated with $$\mathcal{L}$$ -Splines and Steklov-Poincaré Operator in Two Dimensions ⋮ Some examples of kinetic schemes whose diffusion limit is Il'in's exponential-fitting ⋮ An interpretation of the Scharfetter-Gummel finite difference scheme ⋮ \(\mathcal L\)-splines and viscosity limits for well-balanced schemes acting on linear parabolic equations ⋮ Approximation of derivatives in a convection-diffusion two-point boundary value problem ⋮ Aliasing and two-dimensional well-balanced for drift-diffusion equations on square grids

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