半离散有限元逼近的误差估计
Error estimates for semi-discrete finite element approximations for a moving boundary problem capturing the penetration of diffusants into rubber
摘要：
本文考虑了一个描述溶剂在橡胶中扩散的动力学条件的移动边界问题，并研究了相应的弱解的半离散有限元逼近。我们报告的先验和后验误差估计的扩散剂的质量浓度，并分别为一个先验的未知位置的移动边界。我们的工作技术包括积分和能量为基础的估计的非线性抛物型问题提出了一个变换的固定域结合适当使用的插值跟踪不等式来处理的接口条款。我们的有限元近似的数值说明是在实验范围内，并与我们的理论研究显示出良好的一致性。这项工作是一个必要的初步调查之前，扩展目前的移动边界建模，以明确说明超弹性杆的力学捕捉到的基本弹性体的定向膨胀。
英文摘要：
We consider a moving boundary problem with kinetic condition that describes the diffusion of solvent into rubber and study semi-discrete finite element approximations of the corresponding weak solutions. We report on both a priori and a posteriori error estimates for the mass concentration of the diffusants, and respectively, for the a priori unknown position of the moving boundary. Our working techniques include integral and energy-based estimates for a nonlinear parabolic problem posed in a transformed fixed domain combined with a suitable use of the interpolation-trace inequality to handle the interface terms. Numerical illustrations of our FEM approximations are within the experimental range and show good agreement with our theoretical investigation. This work is a preliminary investigation necessary before extending the current moving boundary modeling to account explicitly for the mechanics of hyperelastic rods to capture a directional swelling of the underlying elastomer.
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