Goal-oriented a posteriori error estimation for the biharmonic problem based on an equilibrated moment tensor. (English) Zbl 1524.65845
Summary: In this article, we discuss goal-oriented a posteriori error estimation for the biharmonic plate bending problem. The error for a numerical approximation of a goal functional is represented by several computable estimators. One of these estimators is obtained using the dual-weighted residual method, which takes advantage of an equilibrated moment tensor. Then, an abstract unified framework for the goal-oriented a posteriori error estimation is derived based on the equilibrated moment tensor and the potential reconstruction that provides a guaranteed upper bound for the error of a numerical approximation for the goal functional. In particular, \(C^0\) interior penalty and discontinuous Galerkin finite element methods are employed for the practical realisation of the estimators. Numerical experiments are performed to illustrate the effectivity of the estimators.
MSC:
| 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 |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 31A30 | Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions |
| 74K20 | Plates |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
Keywords:
quantity of interest; a posteriori error estimate; guaranteed bound; equilibrated moment tensor; unified framework; adaptivityReferences:
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