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New iterative solution methods are proposed for the finite element approximation of a class of variational inequalities with nonlinear diffusion-convection operator and constraints to the gradient of solution. Implementation of every iteration of these methods reduces to the solution of a system of linear equations and a set of two-dimensional minimization problems. Convergence is proved by the application of a general result on the convergence of the iterative methods for a nonlinear constrained saddle point problem.

russian journal of numerical analysis and mathematical modelling

Easily implementable iterative methods for variational inequalities with nonlinear diffusion–convection operator and constraints to the gradient of solution