Recent experiences with error estimation and adaptivity. II: Error estimation for \(h\)-adaptive approximations on grids of triangles and quadrilaterals. (English) Zbl 0782.65127
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.
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.
Reviewer: J.Vaníček (Praha)
MSC:
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
Keywords:
adaptive grid; flux iteration; Poisson equation; error estimators; plane elastostatics; flux projection; numerical experimentsCitations:
Zbl 0764.65064References:
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