标题： 分数阶粘弹性波传播的快速全离散有限元方法分析 显示英文标题

标题： Analysis of a fast fully discrete finite element method for fractional viscoelastic wave propagation

摘要： 本文致力于对一种分数次粘弹性波传播模型的数值分析，该模型推广了分数阶麦克斯韦模型和分数阶齐纳模型。 首先，我们将模型问题转化为速度型积分微分方程，并建立其解的存在性、唯一性和正则性。 然后我们考虑一种符合的线性/双线性/三线性有限元半离散方案以及一种使用指数和（SOE）近似处理卷积积分的后向欧拉全离散快速方案，并推导出半离散和全离散方案的误差估计。 最后，我们提供几个数值例子来验证理论结果。 显示英文摘要

摘要： This paper is devoted to a numerical analysis of a fractional viscoelastic wave propagation model that generalizes the fractional Maxwell model and the fractional Zener model. First, we convert the model problem into a velocity type integro-differential equation and establish existence, uniqueness and regularity of its solution. Then we consider a conforming linear/bilinear/trilinear finite element semi-discrete scheme and a fast scheme of backward Euler full discretization with a sum-of-exponentials (SOE) approximation for the convolution integral, and derive error estimates for the semi-discrete and fully discrete schemes. Finally, we provide several numerical examples to verify the theoretical results.