MULTI-GRID METHODS FOR NON-LINEAR ELLIPTIC VARIATIONAL INEQUALITIES

This work concernsthestudyofaclassofvariationalinequalities,in the sense that the obstacle doesnotdependonthesolution,byapplyingthemulti-gridmethodsV-cycleand W-cycle. Multi-grid methodsconsistinsuccessivelyusinggrids(ormeshes)ofdifferentsizes,so as toobta in adetailedsolutioninthehighfrequencies,whileensuringarapidrelaxationof the lowf requencies. Multi-grid methodshavebeenstudiedforlinearellipticalproblems.Forourpart,we are interestedinfinitedifferenceapproximation,byintroducingmulti-gridalgorithms,for non-linear variationalinequalities,insofarasthenon-coerciveandlinearoperator,thesec- ond memberdependsonthesolutionthemixtureofthelasttwocasesandthelastcase where theoperatorandthesecondmemberarenon-linear.