Geodesic
Verification of functional a posteriori error estimates for obstacle problem in 1D
Kybernetika, Tome 49 (2013) no. 5, pp. 738-754

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We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error of approximation is bounded from above by a majorant error estimate. The sharpness of the majorant error estimate is discussed.
Classification : 34B15, 49J40, 49M25, 65K15, 65L60, 74K05, 74M15, 74S05
Keywords: obstacle problem; a posteriori error estimate; functional majorant; finite element method; variational inequalities; Uzawa algorithm 
@article{KYB_2013__49_5_a4,
     author = {Harasim, Petr and Valdman, Jan},
     title = {Verification of functional a posteriori error estimates for obstacle problem in {1D}},
     journal = {Kybernetika},
     pages = {738--754},
     publisher = {mathdoc},
     volume = {49},
     number = {5},
     year = {2013},
     mrnumber = {3182637},
     zbl = {1278.49035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2013__49_5_a4/}
}
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Harasim, Petr; Valdman, Jan. Verification of functional a posteriori error estimates for obstacle problem in 1D. Kybernetika, Tome 49 (2013) no. 5, pp. 738-754. http://geodesic.mathdoc.fr/item/KYB_2013__49_5_a4/