Mesh sensitivity of finite element solution for linear elliptic partial differential equations is analyzed. A bound for the change in the finite element solution is obtained in terms of the mesh deformation and its gradient. The bound shows how the finite element solution changes continuously with the mesh. The result holds in any dimension and for arbitrary unstructured simplicial meshes, general linear elliptic partial differential equations, and general finite element approximations.

翻译：对线性椭圆部分差异方程的有限元素溶液的网格敏感度进行了分析,以网状变形及其梯度为条件对有限元素溶液的改变进行约束。约束显示有限元素溶液如何随着网状而不断变化。结果包含任何维度和任意的不结构的简化中间线、一般的线性椭圆部分差异方程和一般的有限元素近似值。