A New Family of Mixed Finite Elements for the Linear Elastodynamic Problem

We construct and analyze a new family of quadrangular (in two dimensions) or cubic (in three dimensions) mixed finite elements for the approximation of elastic wave equations. Our elements lead to explicit schemes (via mass lumping), after time discretization, including in the case of anisotropic me...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 2002, Vol.39 (6), p.2109-2132
Main Authors: Bécache, E., Joly, P., Tsogka, C.
Format: Article
Language:English
Subjects:
Approximation
Classical and quantum physics: mechanics and fields
Classical mechanics of continuous media: general mathematical aspects
Degrees of freedom
Elastodynamics
Exact sciences and technology
Finite element method
Lagrange multiplier
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical simulation
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Physics
Polynomials
Sciences and techniques of general use
Stress tensors
Symmetry
Tensors
Velocity
Vertices
Waves and wave propagation: general mathematical aspects
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Summary:We construct and analyze a new family of quadrangular (in two dimensions) or cubic (in three dimensions) mixed finite elements for the approximation of elastic wave equations. Our elements lead to explicit schemes (via mass lumping), after time discretization, including in the case of anisotropic media. Error estimates are given for these new elements.
ISSN:0036-1429
1095-7170
DOI:10.1137/S0036142999359189