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The Backward Euler Fully Discrete Finite Volume Method for the Problem of Purely Longitudinal Motion of a Homogeneous Bar

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  • Ziwen Jiang
  • Deren Xie

Abstract

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 an give optimal order error estimates in L2 and H1 norms. Furthermore, we obtain the superconvergence error estimate of the generalized projection of the solution u in H1 norm. Numerical experiment illustrates the convergence and stability of this scheme.

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Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:475801
DOI: 10.1155/2012/475801
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