Adaptive inexact semismooth Newton method for variational inequalities

semismooth_Newton_precision

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

semismooth_Newton_estimators

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

semismooth_Newton_iterations

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

semismooth_Newton_iterations_cum

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):

  • model steady system of variational inequalities, linear constraints: preprint
  • model unsteady system of variational inequalities, linear constraints: preprint
  • compositional two-phase flow in porous media, nonlinear constraints: preprint

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