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A Reduced Local Discontinuous Galerkin Method for Nearly Incompressible Linear Elasticity

机译：近似不可压缩线性弹性的简化局部不连续Galerkin方法

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摘要

A reduced local discontinuous Galerkin (RLDG) method for nearly incompressible linear elasticity is proposed in this paper, which is locking-free. RLDG method can be formally regarded as a special case of LDG method with C_(11) =0. However, RLDG method is actually not covered by LDG method, where C_(11) must be chosen to be positive to ensure the stability of LDG method. RLDG method can also be considered as the localization of some symmetric nonconforming mixed finite element method. The implementation of RLDG method is discussed. By introducing a lifting operator as LDG method, RLDG method can be rewritten as primal formulation with unknown displacement only. Next, we obtain that the convergence rates of the approximation to stress tensor in energy norm and displacement in L~2-norm are O(h~k) and O(h~(k+1)), respectively, which are both uniform with respect to A. Moreover, we obtain a H(div)-conforming displacement by projecting the displacement and corresponding numerical trace of RLDG method into the Raviart-Thomas element space. And then we analyze the error estimates of this postprocessed displacement in H(div)-seminorm and L~2-norm, which are also uniform with respect to λ. Finally, some numerical results are shown to demonstrate the theoretical results.
机译：本文提出了一种用于近似不可压缩线性弹性的简化局部不连续伽勒金（RLDG）方法，该方法是无锁的。可以将RLDG方法正式视为C_（11）= 0的LDG方法的特例。但是，LDG方法实际上并未涵盖RLDG方法，为了确保LDG方法的稳定性，必须选择C_（11）为正数。 RLDG方法也可以看作是某些对称非协调混合有限元方法的局部化。讨论了RLDG方法的实现。通过引入提升算子作为LDG方法，RLDG方法可以重写为仅具有未知位移的原始公式。接下来，我们得出能量范数中应力张量的近似收敛速度和L〜2-范数中的位移的收敛速度分别为O（h〜k）和O（h〜（k + 1）），两者均一致关于A。此外，我们通过将位移和RLDG方法的相应数值轨迹投影到Raviart-Thomas元素空间中来获得符合H（div）的位移。然后，我们分析了H（div）-seminorm和L〜2-norm中这些后处理位移的误差估计，它们相对于λ是一致的。最后，一些数值结果表明了理论结果。

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  • 来源
    《Mathematical Problems in Engineering》 |2013年第3期|546408.1-546408.11|共11页
  • 作者

    Xuehai Huang;

  • 作者单位

    College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China;

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