Adaptive Finite Element Analysis of Incompressible Viscous Flow Using Posteriori Error Estimation and Control of Node Density Distribution.

A posteriori error control in low-order finite element discretisations of incompressible stationary flow problems

Computable a posteriori error bounds and related adaptive meshrefining algorithms are provided for the numerical treatment of monotone stationary flow problems with a quite general class of conforming and nonconforming finite element methods. A refined residual-based error estimate generalises the works of Verfürth; Dari, Duran and Padra; Bao and Barrett. As a consequence, reliable and efficien...

Adaptive Finite Elements for State-Constrained Optimal Control Problems - Convergence Analysis and A Posteriori Error Estimation

A unifying theory of a posteriori finite element error control

Residual-based a posteriori error estimates are derived within a unified setting for lowest-order conforming, nonconforming, and mixed finite element schemes. The various residuals are identified for all techniques and problems as the operator norm ‖`‖ of a linear functional of the form

A Posteriori Finite Element Error Estimation for Diffusion Problems

Adjerid et al. 2] and Yu 19, 20] show that a posteriori estimates of spatial discretiza-tion errors of piecewise bi-p polynomial nite element solutions of elliptic and parabolic problems on meshes of square elements may be obtained from jumps in solution gradients at element vertices when p is odd and from local elliptic or parabolic problems when p is even. We show that these simple error esti...

A Posteriori Error Estimation for Adaptive Iga Boundary Element Methods

A posteriori error estimation and adaptive mesh-refinement are well-established and important tools for standard boundary element methods (BEM) for polygonal boundaries and piecewise polynomial ansatz functions (see e.g. the seminal work [1] for the derivation of the weighted-residual error estimator and [5] for convergence even with optimal rates). In contrast, the mathematically reliable a po...