Superconvergence for the gradient of finite element approximations by L\(^{2}\) projections. (English) Zbl 1047.65095
The authors propose and analyze a gradient recovery technique for finite element solutions which provides new gradient approximations with high order of accuracy. They modify the method of O. C. Zienkiewicz and J. Z. Zhu [Comput. Methods Appl. Mech. Eng. 101, No. 1–3, 207–224 (1992; Zbl 0779.73078)] by applying a global least-squares fitting to the gradient of finite element approximation and provide a theoretical analysis for the modified Zienkiewicz-Zhu method by establishing a superconvergence estimate for the recovered gradient/flux on general quasi-uniform meshes. They also give numerical results to show that the recovery technique is robust and efficient.
Reviewer: Ziwen Jiang (Shandong)
MSC:
65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
65N15 | Error bounds for boundary value problems involving PDEs |
65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
35J25 | Boundary value problems for second-order elliptic equations |