Numerical solution for an aggregation equation with degenerate diffusion
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized nite element method together with a mass lumping technique and an extra stabilizing term plus a semi{implicit Euler time integration....
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/89765 |
| Acceso en línea: | https://hdl.handle.net/11441/89765 https://doi.org/10.1016/j.amc.2020.125145 |
| Access Level: | acceso abierto |
| Palabra clave: | Finite-element approximation Aggregation equation Nonlinear diffusion |
| Sumario: | A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized nite element method together with a mass lumping technique and an extra stabilizing term plus a semi{implicit Euler time integration. Then we carry out a rigorous passage to the limit as the spatial and temporal discretization parameters tend to zero, and show that the sequence of nite element approximations converges toward the unique weak solution of the model at hands. In doing so, nonnegativity is attained due to the stabilizing term and the acuteness on partitions of the computational domain, and hence a priori energy estimates of nite element approximations are established. As we deal with a nonlinear problem, some form of strong convergence is required. The key compactness result is obtained via an adaptation of a Riesz-Fréchet-Kolmogorov criterion by perturbation. A numerical example is also presented. |
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