We present two parallel algorithms based on the domain decomposition methodfor solving a variational inequality over a closed convex cone. First, construct an opencovering {Ω_i} of the original domain Ω∶Ω=\cap_{i=1}^m \Omega_i, where Ω_i,i=1,…,m, are overlapping. i.e. for each Ω_i there exists at least one Ω_j(j≠i) such that Ω_i∩Ω_i≠φ. Choosing an initial guess u~0 for the solution u, we solve parallelly the inequality in each subdomain Ω_i(i=1,…,m) to obtain m corrections. Take an appropriate average of these m corrections as a correctionover Ω and hence obtain a new approximation to u. In this paper we discuss the convergenceof the continuous problem and also the corresponding discrete problem which is obtained by the finite element method.

We present two parallel algorithms based on the domain decomposition methodfor solving a variational inequality over a closed convex cone. First, construct an opencovering {Ω_i} of the original domain Ω∶Ω=\cap_{i=1}^m \Omega_i, where Ω_i,i=1,…,m, are overlapping. i.e. for each Ω_i there exists at least one Ω_j(j≠i) such that Ω_i∩Ω_i≠φ. Choosing an initial guess u~0 for the solution u, we solve parallelly the inequality in each subdomain Ω_i(i=1,…,m) to obtain m corrections. Take an appropriate average of these m corrections as a correctionover Ω and hence obtain a new approximation to u. In this paper we discuss the convergenceof the continuous problem and also the corresponding discrete problem which is obtained by the finite element method.