An adaptive mesh refinement of quadrilateral finite element meshes based upon a posteriori error estimation of quantities of interest: linear static response

2004 ◽  
Vol 20 (1) ◽  
pp. 31-37 ◽  
Author(s):  
Mark E. Botkin ◽  
Hui-Ping Wang
Keyword(s):  
Finite Element ◽  
Adaptive Mesh Refinement ◽  
Adaptive Mesh ◽  
Posteriori Error ◽  
A Posteriori ◽  
Posteriori Error Estimation ◽  
Static Response ◽  
A Posteriori Error ◽  
Quadrilateral Finite Element ◽  
Quantities Of Interest

scholarly journals Flux recovery for Cut finite element method and its application in a posteriori error estimation

2021 ◽  
Author(s):  
Daniela Capatina ◽  
Cuiyu He
Keyword(s):  
Finite Element ◽  
Adaptive Mesh Refinement ◽  
Adaptive Mesh ◽  
Posteriori Error ◽  
Numerical Results ◽  
Error Estimator ◽  
A Posteriori ◽  
Posteriori Error Estimator ◽  
A Posteriori Error ◽  
The Difference

In this article, we aim to recover locally conservative and $H(div)$ conforming fluxes for the linear  Cut Finite Element Solution with Nitsche's method for Poisson problems with Dirichlet boundary condition. The computation of the conservative flux in the Raviart-Thomas space is completely local and does not require to solve any mixed problem. The $L^2$-norm of the difference between the numerical flux and the recovered flux can then be used as a posteriori error estimator in the adaptive mesh refinement procedure. Theoretically we also prove the global reliability and local efficiency. The theoretical results are verified in the numerical results. Moreover, in the numerical results we also observe optimal convergence rate for the flux error.

Sign in / Sign up

Export Citation Format

Share Document