广义神经传播方程H^1-Galerkin低阶非协调混合有限元的超收敛分析  

Superconvergence Analysis of the Lowest Order H^1-Galerkin Nonconforming Mixed Finite Element for Generalized Nerve Conduction Type Equations

作　　者：周树克[1] 王婷[2] 

机构地区：[1]河南城建学院数理学院,河南平顶山467036 [2]南阳师范学院数学与统计学院,河南南阳473061

出　　处：《信阳师范学院学报（自然科学版）》2015年第4期482-485,共4页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11271340);河南省高等学校重点科研项目(15A110012)

摘　　要：利用EQrot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H1模及中间变量p→在H(div;Ω)模意义下的超逼近性质和整体超收敛结果.By employing EQrot element and zero-order Raviart-Thomas element,H1-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 EQrot element,the known high accuracy analysis of zero-order R-T element and the post processing technique,the superclose and superconvergence properties for uin H1-norm and p→in H（div;Ω）-norm were obtained for the above scheme.

关 键 词：广义神经传播方程 H1-Galerkin方法 低阶非协调混合元 半离散与全离散 

分 类 号：O242.21[理学—计算数学]