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Jiang, Ziwen; Xie, Deren

The backward Euler fully discrete finite volume method for the problem of purely longitudinal motion of a homogeneous bar. (English) Zbl 1325.74158

Abstr. Appl. Anal. 2012, Article ID 475801, 23 p. (2012).
Summary: We present a linear backward Euler fully discrete finite volume method for the initial-boundary-value problem of purely longitudinal motion of a homogeneous bar and give an optimal order error estimates in \(L^2\) and \(H^1\) norms. Furthermore, we obtain the superconvergence error estimate of the generalized projection of the solution \(u\) in \(H^1\) norm. Numerical experiment illustrates the convergence and stability of this scheme.

MSC:

74S10 Finite volume methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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\textit{Z. Jiang} and \textit{D. Xie}, Abstr. Appl. Anal. 2012, Article ID 475801, 23 p. (2012; Zbl 1325.74158)
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References:

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