论文标题
用于一类Evolution微分方程的混合有限元方法，带有$ P $ -laplacian和内存
A Mixed Finite Element Method for a Class of Evolution Differential Equations with $p$-Laplacian and Memory
论文作者
论文摘要
我们为一类带有$ p $ laplacian和非线性内存的抛物线方程式提供了一种新的混合有限元方法。研究了该方法的适用性，稳定性和收敛性。首先，该问题以混合配方为一个抛物线方程和伏特拉方程的系统。然后，使用Lagrangian $ r \ geq1 $的Lagrangian的有限元方法在空间变量中离散化。最后，使用带有梯形正交的cranck-nicolson方法用于离散时间变量。对于每种方法，我们建立解决方案的存在，独特性和规律性。发现收敛顺序取决于$ p $ -laplacian上的参数$ p $，因为它随着$ p $的增加而降低。
We present a new mixed finite element method for a class of parabolic equations with $p$-Laplacian and nonlinear memory. The applicability, stability and convergence of the method are studied. First, the problem is written in a mixed formulation as a system of one parabolic equation and a Volterra equation. Then, the system is discretized in the space variable using the finite element method with Lagrangian basis of degree $r\geq1$. Finally, the Cranck-Nicolson method with the trapezoidal quadrature is applied to discretize the time variable. For each method, we establish existence, uniqueness and regularity of the solutions. The convergence order is found to be dependent on the parameter $p$ on the $p$-Laplacian in the sense that it decreases as $p$ increases.
