Convergence of a fully discrete and energy-dissipating finite-volume scheme for aggregation-diffusion equations. (English) Zbl 1460.65160
Summary: We study an implicit finite-volume scheme for nonlinear, non-local aggregation-diffusion equations which exhibit a gradient-flow structure, recently introduced in our work [Commun. Math. Sci. 18, No. 5, 1259–1303 (2020; Zbl 1467.35317)]. Crucially, this scheme keeps the dissipation property of an associated fully discrete energy, and does so unconditionally with respect to the time step. Our main contribution in this work is to show the convergence of the method under suitable assumptions on the diffusion functions and potentials involved.
MSC:
| 65R20 | Numerical methods for integral equations |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 45K05 | Integro-partial differential equations |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
finite-volume methods; convergence of numerical methods; drift-diffusion equations; integro-differential equationsCitations:
Zbl 1467.35317References:
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