 Error components for exact semismooth Newton (left), inexact semismooth Newton (middle), and adaptive inexact semismooth Newton (right) in function of mesh refinement, model steady system of variational inequalities |
 A posteriori error estimators in function of algebraic solver iterations (left) and semismooth Newton iterations (right) for the exact/inexact/adaptive inexact semismooth Newton methods, model steady system of variational inequalities |
 Number of semismooth Newton iterations (left) and cumulated number of algebraic solver iterations (right) for the exact/inexact/adaptive inexact semismooth Newton methods, model steady system of variational inequalities |
 Cumulated number of semismooth Newton iterations (left) and cumulated number of algebraic solver iterations (right) for the exact/inexact/adaptive inexact semismooth Newton methods, unsteady nonlinear system of variational inequalities modeling compositional two-phase flow in porous media with exchange of components between the phases |
Main results:
- guaranteed upper bound on the total error;
- distinction of different error components (spatial discretization, temporal discretization, semismooth Newton linearization, algebraic solver);
- design of an adaptive inexact semismooth Newton method for variational inequalities;
- application to unsteady nonlinear coupled degenerate variational inequalities (compositional two-phase flow in porous media with exchange of components between the phases).
Details in Ph.D. thesis of Jad Dabaghi, Ph.D. defense presentation; with Vincent Martin (and Ibtihel Ben Gharbia):
