2014/03/26 by Petr Harasim, Harasim, Petr, Jan Valdman +1
Engineering · Mathematics · Medicine · #65M15 #65N30 #74K15 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Management of metastatic bone disease #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1403.6619
openalex publication_date 2014/03/26 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28
We verify functional a posteriori error estimate proposed by S. Repin for a\nclass of obstacle problems. The obstacle problem is formulated as a quadratic\nminimization problem with constrains equivalently formulated as a variational\ninequality. New benchmarks with known analytical solutions in 2D are\nconstructed based on 1D benchmark introduced by P. Harasim and J. Valdman.\nNumerical approximation of the obstacle problem is obtained by the finite\nelement method using bilinear elements on a rectangular mesh. Error of the\napproximation is meassured in the energy norm and bounded from above by a\nfunctional majorant, whose value is minimized with respect to unknown gradient\nfield discretized by Raviart-Thomas elements and Lagrange multipliers field\ndiscretized by piecewise constant functions.\n