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#### Convergence of a goal-oriented adaptive finite element method for semilinear PDE

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**Speaker(s)**Yunrong Zhu (Idaho State University)**Date**From 2014-06-26 To 2014-06-26**Venue**Room 77201 at #78 courtyard, Beijing International Center for Mathematical Research

Speaker: Yunrong Zhu (Idaho State University)

Time: Thu, 06/26/2014 - 15:30

Place: Room 77201 at #78 courtyard, Beijing International Center for Mathematical Research

Abstract: In this talk, we develop convergence theory for a class of goal-oriented adaptive ﬁnite element (GOFEM) algorithms for second order semilinear elliptic equations. One of the main challenges in the nonlinear problem that we don’t see in the linear case is the dependence of the dual problem on the exact solution. As it is not practical to work with a dual problem we can not compute, we develop a practical adaptive algorithm in which the mesh reﬁnement is driven both by residual-based estimator for the approximation of the primal solution, and in a sequence of approximate dual problems which relies only on the numerical solution obtained from the previous step. We show the contraction of the adaptive ﬁnite element algorithm. Numerical experiments support the theoretical results.