Some methods for the numerical solution of variational inequalities with two obstacles

In this paper the problem \(\mathop {\min }\limits_{u \in K} \int\limits_\Omega {\left| {u_x } \right|^z dx} \) is studied. HereK≡{u∈W ₀ ¹ (Ω):ψ _i≤u≤ψ ₂}, whereψ ₁ andψ ₂ are given functions. The finite-dimensional discretization has been carried out both by the classical finite-difference method and by a «dnal» method whose corresponding finite-dimensional problem is solved by some new method in quadratic programming.