The local bounded commuting projection operators of nonstandard finite element de Rham complexes in two and three dimensions are constructed systematically. The assumptions of the main result are mild and can be verified. For three dimensions, the result can be applied to the standard finite element de Rham complex, Hermite complex, Argyris complex and Neilan's Stokes complex. For two dimensions, the result can be applied to the Hermite--Stenberg complex and the Falk--Neilan Stokes complex.
翻译:非标准限量元素拉姆综合体两维和三个维度的非标准限量元素的当地封闭通勤预测操作员系统构建,主要结果的假设是温和的,可以核实。对于三个维度,其结果可适用于标准限量元素拉姆综合体、Hermite综合体、Argyris综合体和Neilan的斯托克斯综合体。对于两个维度,其结果可适用于Hermite-Stenberg综合体和Falk-Neiran Stokes综合体。</s>