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On the error estimate of nonconforming finite element approximation to the obstacle problem. (English) Zbl 1053.65049
Finite element approximations with nonconforming linear elements on a triangular grid as well as Wilson elements on rectangular grids are applied to 2-dimensional obstacle problems. The original inequality constrained problem is replaced by the finite element one using the related broken bilinear form. The obstacle condition in the discrete problems is enforced in the midpoints of the inner edges. Estimates of order h are derived in terms of the broken norm for both discretizations.
MSC:
65K10Optimization techniques (numerical methods)
49J20Optimal control problems with PDE (existence)
49M15Newton-type methods in calculus of variations