A numerical-analysis-focused comparison of several finite volume schemes for a unipolar degenerate drift-diffusion model
Clément Cancès, Claire Chainais-Hillairet, Jürgen Fuhrmann, Benoît Gaudeul
Abstract
Abstract In this paper we consider a unipolar degenerate drift-diffusion system where the relation between the concentration of the charged species $c$ and the chemical potential $h$ is $h(c)=\log \frac{c}{1-c}$. We design four different finite volume schemes based on four different formulations of the fluxes. We provide a stability analysis and existence results for the four schemes. The convergence proof with respect to the discretization parameters is established for two of them. Numerical experiments illustrate the behaviour of the different schemes.
Topics & Concepts
Degenerate energy levelsDiscretizationDiffusionStability (learning theory)Convergence (economics)Finite volume methodMathematicsApplied mathematicsVolume (thermodynamics)Statistical physicsMathematical analysisPhysicsMechanicsThermodynamicsComputer scienceQuantum mechanicsEconomicsMachine learningEconomic growthGas Dynamics and Kinetic TheoryComputational Fluid Dynamics and AerodynamicsAdvanced Mathematical Modeling in Engineering