Numerical analysis of a method for solving 2D linear isotropic elastodynamics with traction free boundary condition using potentials and finite elements

DOI10.1090/mcom/3613OpenAlexW3165214515WikidataQ114094317 ScholiaQ114094317MaRDI QIDQ4992225

Jorge Albella Martínez, Patrick Joly, Sebastien Imperiale, Jerónimo Rodríguez

Publication date: 7 June 2021

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/mcom/3613

zbMATH Keywords

CFL conditionHelmholtz decompositionnumerical analysismass lumpingpotentialselastic wave propagationstability of the evolution problem

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Wave equation (35L05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Linear waves in solid mechanics (74J05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (4)

A virtual element method for the solution of 2D time-harmonic elastic wave equations via scalar potentials ⋮ Space-time methods for time-dependent partial differential equations. Abstracts from the workshop held February 6--12, 2022 ⋮ Numerical approximation of a potentials formulation for the elasticity vibration problem ⋮ An efficient numerical method for time domain electromagnetic wave propagation in co-axial cables

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Solving 2D linear isotropic elastodynamics by means of scalar potentials: a new challenge for finite elements
• Generalized inverses. Theory and applications.
• Higher Order Triangular Finite Elements with Mass Lumping for the Wave Equation
• Finite Element Methods for Navier-Stokes Equations
• Numerical Methods for the First Biharmonic Equation and for the Two-Dimensional Stokes Problem
• Analysis of Mixed Methods Using Mesh Dependent Norms
• Mixed and Hybrid Finite Element Methods
• Solving the homogeneous isotropic linear elastodynamics equations using potentials and finite elements. The case of the rigid boundary condition
• The Mathematical Theory of Finite Element Methods
• Discretization methods and iterative solvers based on domain decomposition

This page was built for publication: Numerical analysis of a method for solving 2D linear isotropic elastodynamics with traction free boundary condition using potentials and finite elements