| Abstract: |
| The main part of the talk consists of an adaptive mesh-refining based on the multi-level algorithm and derive a unified a posteriori error estimate for a class of nonlinear problems in the abstract setting. The multi-level algorithm on adaptive meshes retains quadratic convergence of Newton`s method across different mesh levels both theoretically and numerically.
As applications of our theory, we consider the pseudostress-velocity formulation of Navier-Stokes equations and the standard Galerkin formulation of semilinear elliptic equations. Reliable and efficient a posteriori error estimators for both approximations are derived. Several numerical examples are presented to test the performance of the algorithm and validity of the theory developed. Lastly, ongoing work on Darcy-Forchheimer flows is presented. |
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