We consider mixed finite element methods for linear elasticity where the symmetry of the stress tensor is weakly enforced. Both an a priori and a posteriori error analysis are given for several known families of methods that are uniformly valid in the incompressible limit. Based on the Prager-Singe hypercircle principle, an a posteriori estimate with explicitly known constants is derived. The results are verified by numerical examples.
翻译:我们考虑对线性弹性采用混合的有限元素方法,在对应应应力强度的对称性执行不力的情况下,对若干已知的、在不可压缩限度内统一有效的方法组进行先验和后验错误分析。根据Prager-Singe 超圆环原则,得出一个带有明确已知常数的后验估计。结果通过数字示例加以验证。