Finite element approximation and analysis of a viscoelastic scalar wave equation with internal variable formulations
DOI10.1016/j.cam.2022.114340zbMath1489.74056arXiv2001.04745OpenAlexW4226087208WikidataQ113878727 ScholiaQ113878727MaRDI QIDQ2141612
Publication date: 25 May 2022
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2001.04745
linear viscoelasticitya priori error estimateinternal variablestability boundCrank-Nicolson time discretization schemeGalerkin spatial finite element method
Finite element methods applied to problems in solid mechanics (74S05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Linear constitutive equations for materials with memory (74D05) Finite difference methods applied to problems in solid mechanics (74S20) Linear waves in solid mechanics (74J05) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)
Uses Software
Cites Work
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- Galerkin finite element methods for parabolic problems
- On inequalities of Korn, Friedrichs and Babuska-Aziz
- Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
- Numerical methods for hyperbolic and parabolic integro-differential equations
- Equilibrium finite elements for the linear elastic problem
- Discontinuous Galerkin finite element methods for linear elasticity and quasistatic linear viscoelasticity
- An \textit{a priori} error estimate for a temporally discontinuous Galerkin space-time finite element method for linear elasto- and visco-dynamics
- An abstract Volterra equation with applications to linear viscoelasticity
- A posteriori error estimates for space-time finite element approximation of quasistatic hereditary linear viscoelasticity problems
- ANALYTIC REGULARITY FOR LINEAR ELLIPTIC SYSTEMS IN POLYGONS AND POLYHEDRA
- Viscoelastic Functionally Graded Materials Subjected to Antiplane Shear Fracture
- Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
- Finite element methods for parabolic and hyperbolic partial integro-differential equations
- On Korn's second inequality
- Linear Finite Element Methods for Planar Linear Elasticity
- Error Estimates with Sharp Constants for a Fading Memory Volterra Problem in Linear Solid Viscoelasticity
- Numerical Solution of Linear Quasistatic Hereditary Viscoelasticity Problems
- Discontinuous Galerkin finite element methods for dynamic linear solid viscoelasticity problems
- A Priori $L_2 $ Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations
- On Korn's inequality
- Optimal long-time \(L_p(0,T)\) stability and semidiscrete error estimates for the Volterra formulation of the linear quasistatic viscoelasticity problem
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