强非线性传热问题与摩擦的自适应FE-BE耦合 II
Adaptive FE-BE coupling for strongly nonlinear transmission problems with friction II
AI总结：
本文研究了非线性弹性中传热或接触问题的有限元与边界元耦合的well-posedness和误差分析，针对具有无界应力-应变关系的W^{1,p}-单调Hencky材料，提出了一种泛函分析框架，得到伽辽金近似解的先验和后验误差估计。
摘要：
本文讨论了有限元和边界元耦合在非线性弹性中传热或接触问题的well-posedness和误差分析。它关注W^{1,p}-单调Hencky材料，这些材料出现在冰盖、非牛顿流体或多孔介质建模中。对于1<p<2，边界元方法的二次型在与非线性算子相关的自然函数空间中不连续。我们提出了一种数值分析的泛函分析框架，得到由此产生的边界/域变分不等式伽辽金近似解的先验和后验误差估计。后验估计补充了最近在线弹性摩擦问题混合有限元格式中获得的估计。
英文摘要：
This article discusses the well-posedness and error analysis of the coupling of finite and boundary elements for transmission or contact problems in nonlinear elasticity. It concerns W^{1,p}-monotone Hencky materials with an unbounded stress-strain relation, as they arise in the modelling of ice sheets, non-Newtonian fluids or porous media. For 1<p<2 the bilinear form of the boundary element method fails to be continuous in natural function spaces associated to the nonlinear operator. We propose a functional analytic framework for the numerical analysis and obtain a priori and a posteriori error estimates for Galerkin approximations to the resulting boundary/domain variational inequality. The a posteriori estimate complements recent estimates obtained for mixed finite element formulations of friction problems in linear elasticity.
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