On adaptive anisotropic mesh optimisation for convection-diffusion problems
نویسندگان
چکیده
Numerical solution of convection-dominated problems requires the use of layer-adapted anisotropic meshes. Since a priori construction of such meshes is difficult for complex problems, it is proposed to generate them in an adaptive way by moving the node positions in the mesh such that an a posteriori error estimator of the overall error of the approximate solution is reduced. This approach is formulated for a SUPG finite element discretisation of a stationary convection-diffusion problem defined in a two-dimensional polygonal domain. The optimisation procedure is based on the discrete adjoint technique and a SQP method using the BFGS update. The optimisation of node positions is applied to a coarse grid only and the resulting anisotropic mesh is then refined by standard adaptive red-greed refinement. Four error estimators based on the solution of local Dirichlet problems are tested and it is demonstrated that an L norm based error estimator is the most robust one. The efficiency of the proposed approach is demonstrated on several model problems whose solutions contain typical boundary and interior layers.
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