Recent experiences with error estimation and adaptivity. II: Error estimation for \(h\)-adaptive approximations on grids of triangles and quadrilaterals
In part I [ibid. 97, No. 3, 399-436 (1992; Zbl 0764.65064)] residual and flux projection error estimators were presented for the finite element approximations of the solution of the Poisson equation. In the present part further numerical experiments are presented including error estimators for the vector-valued problem of plane elastostatics. A detailed numerical study of several flux-projectors for \(h\)-adaptive grids of bilinear and biquadratic quadrilaterals is conducted. A flux equilibration iteration, which may be employed in some cases to improve flux projection estimates is also included. For the case of grids of quadrilaterals, several versions of the boundary integral term in the definition of the local problems are compared. The numerical experiments confirm the good overall performance of residual estimates, and indicate that flux projection estimates in some interesting situation may be divergent.
scientific article; zbMATH DE number 146811
scientific article