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• W174882013 abstract "This thesis covers three topicsâ��a posteriori error estimation, mixed finite element ap- proximations for anisotropic meshes and the solution of the time-dependent Navier-Stokes equations using a stabilized Q1 â�� P0 approximation.First, we find effective error estimators for (bi-)quadratic approximations for the dif- fusion problem, and (bi-)quadratic velocity and (bi-)linear pressure mixed approximations for incompressible flow problems. The efficiency and reliability of the error estimators are established in the case of the Stokes problem.Second, since standard inf-sup stable mixed approximations typically become unstable for anisotropic meshes, we devote our attention to a stabilized Q1â��P0 approximation, which is introduced by Kechkar and Silvester [Math. Comp., 58, 1â��10, 1992]. We establish a robust a priori error bound for this stabilized Q1 â�� P0 approximation for anisotropic meshes.Finally, the stabilized Q1 â�� P0 approximation is applied to solving time dependent in- compressible flow problems with an adaptive time stepping method introduced by Kay et al. [SIAM J. Sci. Comput., 32, 111â��128, 2010]. The main contribution of this part is to find the optimal stabilization parameter, which is eventually shown to be inversely proportional to the Reynolds number of the flow." @default.
• W174882013 created "2016-06-24" @default.
• W174882013 creator A5014407690 @default.
• W174882013 date "2010-12-09" @default.
• W174882013 modified "2023-09-24" @default.
• W174882013 title "Error estimation and stabilization for low order finite elements" @default.
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