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Structure-preserving finite difference scheme for 1D thermoviscoelastoplastic equations under uniformly distributed temperature

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  • Nagata, Takuto
  • Yoshikawa, Shuji

Abstract

In this article, we investigate a structure-preserving finite difference scheme to the thermo-visco-elasto-plastic system in a one-space dimension under a perfect elasto-plasticity represented by the stop operator. We introduce the structure-preserving finite difference scheme for the system which satisfies the energy conservation law, momentum conservation law and the increasing law of entropy in the discrete sense. The main purpose of this article is to give mathematical treatment such as the existence of solution and error estimate for the scheme, under the assumption of uniformly distributed temperature with respect to space. In addition, several numerical simulations are also demonstrated as examples.

Suggested Citation

  • Nagata, Takuto & Yoshikawa, Shuji, 2023. "Structure-preserving finite difference scheme for 1D thermoviscoelastoplastic equations under uniformly distributed temperature," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 147-168.
    • Handle: RePEc:eee:matcom:v:210:y:2023:i:c:p:147-168
    DOI: 10.1016/j.matcom.2023.03.002
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    1. Yoshikawa, Shuji, 2019. "Remarks on energy methods for structure-preserving finite difference schemes – Small data global existence and unconditional error estimate," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 80-92.
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