Anisotropic residual based a posteriori mesh adaptation in 2D: element based approach
For researchers in computational mechanics and adaptive finite elements, this provides a new anisotropic adaptation approach with improved error control, though it is incremental over existing methods.
The authors develop an element-based anisotropic mesh adaptation method that equidistributes error without using a metric, showing favorable energy norm error control per degree of freedom compared to three popular methods, at the cost of higher CPU usage. A new L2 variant of the estimator is introduced and shown to give better L2 error control.
An element based adaptation method is developed for an anisotropic a posteriori error estimator. The adaptation does not make use of a metric, but instead equidistributes the error over elements using local mesh modifications. Numerical results are reported, comparing with three popular anisotropic adaptation methods currently in use. It was found that the new method gives favourable results for controlling the energy norm of the error in terms of degrees of freedom at the cost of increased CPU usage. Additionally, we considered a new $L^2$ variant of the estimator. The estimator is shown to be conditionally equivalent to the exact $L^2$ error. We provide examples of adapted meshes with the $L^2$ estimator, and show that it gives greater control of the $L^2$ error compared with the original estimator.