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

2025/07/16 by Hao Yuan, Yuan, Hao, Xiaoping Xie +1 · 1 citation
Chemical Engineering · Engineering · #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Rheology and Fluid Dynamics Studies #Vibration and Dynamic Analysis

paper · pdf · doi:10.48550/arxiv.2507.11822

openalex publication_date 2025/07/16 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• A fast fully discrete mixed finite element scheme for fractional viscoelastic models of wave propagation
• Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations
• Well-posedness of an integro-differential equation with positive type kernels modeling fractional order viscoelasticity
• The Finite Element Method for Elliptic Problems
• Time-Domain Finite Element Analysis of Viscoelastic Structures with Fractional Derivatives Constitutive Relations
• Fractional calculus - A different approach to the analysis of viscoelastically damped structures

Cited by

• Variable-order fractional wave equation: Analysis, numerical approximation, and fast algorithm

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