Asymptotically exact a posteriori error estimators for first-order div least-squares methods in local and global L-2 norm

作者：Cai Zhiqiang; Carey Varis; Ku JaEun^*; Park Eun Jae

来源：Computers & Mathematics with Applications, 2015, 70(4): 648-659.

DOI：10.1016/j.camwa.2015.05.010

• Least-squares
• Finite element methods
• Error estimates

A new asymptotically exact a posteriori error estimator is developed for first-order div least-squares (LS) finite element methods. Let (u(h), sigma(h)) be LS approximate solution for (u, sigma = -A del u). Then, epsilon = parallel to A(-1/2)(sigma(h) + A del u(h))parallel to(0) is asymptotically exact a posteriori error estimator for parallel to A(1/2)del(u - u(h))parallel to(0) or parallel to A(-1/2)(sigma - sigma(h))parallel to(0) depending on the order of approximate spaces for sigma and u. For epsilon to be asymptotically exact for parallel to A(1/2)del(u - u(h))parallel to(0), we require higher order approximation property for sigma, and vice versa. When both A del u and sigma are approximated in the same order of accuracy, the estimator becomes an equivalent error estimator for both errors. The underlying mesh is only required to be shape regular, i.e., it does not require quasi-uniform mesh nor any special structure for the underlying meshes. Confirming numerical results are provided and the performance of the estimator is explored for other choice of spaces for (u(h), sigma(h)). Published by Elsevier Ltd.

• 出版日期2015-8