论文标题
标量辅助变量有限元方案用于抛物线抛物线凯勒 - 塞格模型
Scalar auxiliary variable finite element scheme for the parabolic-parabolic Keller-Segel model
论文作者
论文摘要
我们描述并分析了抛物线抛物线凯勒 - 塞格模型的有限元数值方案。标量辅助变量方法用于检索离散级别与系统相关的能量的单调衰减。这种方法依赖于将凯勒 - 塞格模型解释为梯度流。由此产生的数值方案是有效且易于实现的。我们表明存在独特的非负解决方案，并且由于使用SAV方法而获得了修改的离散能量。我们还证明了离散溶液与连续凯勒 - 塞格模型的弱形式的融合。
We describe and analyze a finite element numerical scheme for the parabolic-parabolic Keller-Segel model. The scalar auxiliary variable method is used to retrieve the monotonic decay of the energy associated with the system at the discrete level. This method relies on the interpretation of the Keller-Segel model as a gradient flow. The resulting numerical scheme is efficient and easy to implement. We show the existence of a unique non-negative solution and that a modified discrete energy is obtained due to the use of the SAV method. We also prove the convergence of the discrete solutions to the ones of the weak form of the continuous Keller-Segel model.
