Finite element approximation of solutions to a class of nonlinear hyperbolic–parabolic equations
Copyright policy )Finite element approximation of solutions to a class of nonlinear hyperbolic–parabolic equations
The authors investigate a numerical approximation of \textit{S. S. Antman} and \textit{T. I. Seidman}'s model [J. Differ. Equations 124, No. 1, 132-185 (1996; Zbl 0844.35021)] of the longitudinal motion of a viscoelastic rod. The constitutive assumptions ensure that infinite compressive stress is necessary to produce total compression of the rod. The authors study the regularity of solution of the continuous problem, the convergence of a semi-discrete finite element method, and properties of a space-time finite element scheme. Results of sample computations are also provided.
- University of Cincinnati United States
- University System of Ohio United States
- University of Maryland, Baltimore County United States
regularity of solution, space-time finite element scheme, Finite element methods applied to problems in solid mechanics, Antman-Seidman model, Numerical approximation of solutions of dynamical problems in solid mechanics, viscoelastic rod, infinite compressive stress, Rods (beams, columns, shafts, arches, rings, etc.), convergence of semi-discrete finite element method, numerical approximation
regularity of solution, space-time finite element scheme, Finite element methods applied to problems in solid mechanics, Antman-Seidman model, Numerical approximation of solutions of dynamical problems in solid mechanics, viscoelastic rod, infinite compressive stress, Rods (beams, columns, shafts, arches, rings, etc.), convergence of semi-discrete finite element method, numerical approximation
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