2016/11/08 by Sharat Gaddam, Thirupathi Gudi, Gaddam, Sharat +1
Computer Science · Engineering · #65N15 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Nuclear and radioactivity studies #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1611.02805
openalex publication_date 2016/11/08 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
We propose a new and simpler residual based a posteriori error estimator for\nfinite element approximation of the elliptic obstacle problem. The results in\nthe article are two fold. Firstly, we address the influence of the\ninhomogeneous Dirichlet boundary condition in em a posteriori error control\nof the elliptic obstacle problem. Secondly by rewriting the obstacle problem in\nan equivalent form, we derive simpler em a posteriori error bounds which are\nfree from min/max functions. To accomplish this, we construct a post-processed\nsolution uh of the discrete solution uh which satisfies the exact\nboundary conditions although the discrete solution uh may not satisfy. We\npropose two post processing methods and analyze them. We remark that the\nresults known in the literature are either for the homogeneous Dirichlet\nboundary condition or that the estimator is only weakly reliable in the case of\ninhomogeneous Dirichlet boundary condition.\n