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Convergence of Adaptive Finite Element Methods with Inexact Solvers

Date:
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In this talk, we consider the design of practical adaptive multilevel finite element methods for semilinear elliptic partial differential equations. At each refinement level, the nonlinear system of equations is solved inexactly by Newton/multilevel methods. Under certain assumptions on the inexact solver, we are able to show that the adaptive algorithm still satisfies the a contraction property between two successive refinements. We will also show some numerical evidence of the convergence and accuracy of the overall AFEM algorithm.