Convergence, accuracy and stability of finite element approximations of a class of non‐linear hyperbolic equations

Oden, J. Tinsley; Fost, R. B.

doi:10.1002/nme.1620060307

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Cited by 32 publications

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“…The governing equation is given by (6), with the constitutive relation defined by (7). For comparison, an exact solution of the form…”

Section: Numerical Resultsmentioning

confidence: 99%

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Stability and convergence of some finite element algorithms for nonlinear elastodynamics

Hamdan

Patamapongs

1985

Numerical Meth Engineering

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SUMMARYA series of direct-integration and model-expansion finite element algorithms for a geometrically and materially nonlinear elastodynamic problem are constructed and analysed. The algorithms are constructed by temporally approximating the individual nonlinear stiffness terms such that discrete conservation laws are obtained. This conservative property has a positive effect in providing a stable approximation, and in addition allows the stability properties of the algorithms to be easily assessed. Stability and convergence criteria for the algorithms are rigorously established using an energy method.

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“…The governing equation is given by (6), with the constitutive relation defined by (7). For comparison, an exact solution of the form…”

Section: Numerical Resultsmentioning

confidence: 99%

“…D P -' I 2 ] ) = --(6,DX"+ 6,DX"' ' I 2 ) + +dcn, ,11 ( D Z , DX ) + -(6tDC"-"2,6tDC"-'~2) +~6 s , m~,1 2 ( D Z , D C ) In addition, typical nonlinear relationships of the following form can be derived: STABILITY AND CONVERGENCE OF SOME FINlTE ELEMENT ALGORITHMS 9x7 + (1 + 5 ) ( [ D u n + ( Du" + D u n -) I ,DE", [dtDC"+112 + d,i7) …”

mentioning

confidence: 99%