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<p>The 1D dynamic problem describing discontinuous impact of a&#xa0;rigid obstacle by an elastic bar is considered in the variational formulation. For its numerical solution within the space-time finite element method (STFEM) discretization, the primal-dual active set (PDAS) algorithm is constructed. The piece-wise linear solution given in the closed form, and conservation of the energy provided by persistency conditions, are established on a&#xa0;suitable partition of the space-time domain. Advantages of the suggested variational approach are validated in computational tests of the impact problem on uniform triangle grids in 2D. The numerical result is free of spurious oscillations, not dissipative, indistinguishable from the analytical solution at grid points, and convergent by mesh refinement.</p>

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Space-time finite element based primal-dual active set method for the non-smooth problem of impact of rigid obstacle by elastic bar

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  • 出版模式：

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  • 发表日期：

    2025年1月1日

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  • Victor A. Kovtunenko

摘要

The 1D dynamic problem describing discontinuous impact of a rigid obstacle by an elastic bar is considered in the variational formulation. For its numerical solution within the space-time finite element method (STFEM) discretization, the primal-dual active set (PDAS) algorithm is constructed. The piece-wise linear solution given in the closed form, and conservation of the energy provided by persistency conditions, are established on a suitable partition of the space-time domain. Advantages of the suggested variational approach are validated in computational tests of the impact problem on uniform triangle grids in 2D. The numerical result is free of spurious oscillations, not dissipative, indistinguishable from the analytical solution at grid points, and convergent by mesh refinement.