广义神经传播方程 H1-Galerkin低阶非协调混合有限元的超收敛分析

Superconvergence Analysis of the Lowest Order H1-Galerkin Nonconforming Mixed

  • 摘要: 利用 E Q r o t 和零阶 R - T 元对广义神经传播方程, 建立了 H1-Galerkin低阶非协调混合有限元的半离散格式 . 首先证明了逼近格式解的存在唯一性,然后利用 EQrot 元的特殊性质、 零阶 R - T 元的高精度结果及插值后处理算子,导出了精确解 u 在 H 1 模及中间变量 p→在 H ( d i v ; Ω ) 模意义下的超逼近性质和整体超收敛结果 .

     

    Abstract: By employing EQrotelement and zero-order Raviart-Thomas element, H1-Galerkin nonconforming mixed finite element scheme was discussed for a class of generalized nerve conduction type equations under semi-discrete. The existence and uniqueness of the solution about the approximation scheme were proved. Based on the special characters of EQrotelement, the known high accuracy analysis of zero-order R-T element and the post processing technique, the superclose and  superconvergence properties for u in H1-norm and p→ in H(div;Ω)-norm were obtained for the above scheme

     

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