标题： 混合Nitsche分布式计算 显示英文标题

标题： Hybrid Nitsche for distributed computing

摘要： 我们扩展了文献[1]中基于模型降阶的分布式有限元方法，使用混合Nitsche格式将其推广到任意多项式次数。 该新方法显著简化了大规模问题中将有限元系统转化为约化基的过程。 我们证明，约化的Nitsche解误差在有限元空间的逼近阶上以最优速率收敛，并且在维数约简参数 $\epsilon$ 上线性收敛。 使用二阶多项式基的非平凡四面体网格数值测试支持了理论结果。 显示英文摘要

摘要： We extend the distributed finite element method of [1], built upon model order reduction, to arbitrary polynomial degree using a hybrid Nitsche scheme. This new method considerably simplifies the transformation of the finite element system to the reduced basis for large problems. We prove that the error of the reduced Nitsche solution converges optimally with respect to the approximation order of the finite element spaces and linearly with respect to the dimension reduction parameter $\epsilon$. Numerical tests with nontrivial tetrahedral meshes using second-degree polynomial bases support the theoretical results.