Mesh adaptation based on functional a posteriori estimates with Raviart-Thomas approximation

摘要

Adaptive algorithms based on functional a posteriori estimates for the Dirichlet problem for the stationary diffusion equation with jump discontinuities in the equation coefficients are compared. The algorithms have been implemented in MATLAB with the use of both standard finite element approximations and the zero-order Raviart-Thomas approximation. The adaptation results are analyzed using indicators of the local error distribution. Specifically, sequences of finite-element partitions, effectivity indices of estimates, and relative errors of approximate solutions are compared.