On the inclusion of the recombination term in descretizations of the semiconductor device equations
Mathematics and Computers in Simulation
An atlas of functions
Two-dimensional exponential fitting and applications to drift-diffusion models
SIAM Journal on Numerical Analysis
Semiconductor equations
Analysis of a cell-vertex finite volume method for convection-diffusion problems
Mathematics of Computation
Partial Differential Equations: Modeling, Analysis, Computation (Siam Monographs on Mathematical Modeling and Computation) (Saim Models on Mathematical Modeling and Computation)
Principles of Computational Fluid Dynamics
Principles of Computational Fluid Dynamics
Numerical Mathematics (Texts in Applied Mathematics)
Numerical Mathematics (Texts in Applied Mathematics)
Journal of Computational Physics
Maxwellian Decay for Well-balanced Approximations of a Super-characteristic Chemotaxis Model
SIAM Journal on Scientific Computing
Extension of the Complete Flux Scheme to Systems of Conservation Laws
Journal of Scientific Computing
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We present a new finite volume scheme for the advection-diffusion-reaction equation. The scheme is second order accurate in the grid size, both for dominant diffusion and dominant advection, and has only a three-point coupling in each spatial direction. Our scheme is based on a new integral representation for the flux of the one-dimensional advection-diffusion-reaction equation, which is derived from the solution of a local boundary value problem for the entire equation, including the source term. The flux therefore consists of two parts, corresponding to the homogeneous and particular solution of the boundary value problem. Applying suitable quadrature rules to the integral representation gives the complete flux scheme. Extensions of the complete flux scheme to two-dimensional and time-dependent problems are derived, containing the cross flux term or the time derivative in the inhomogeneous flux, respectively. The resulting finite volume-complete flux scheme is validated for several test problems.