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- W4308670810 abstract "We consider scalar semilinear elliptic PDEs where the nonlinearity is strongly monotone, but only locally Lipschitz continuous. We formulate an adaptive iterative linearized finite element method (AILFEM) which steers the local mesh refinement as well as the iterative linearization of the arising nonlinear discrete equations. To this end, we employ a damped Zarantonello iteration so that, in each step of the algorithm, only a linear Poisson-type equation has to be solved. We prove that the proposed AILFEM strategy guarantees convergence with optimal rates, where rates are understood with respect to the overall computational complexity (i.e., the computational time). Moreover, we formulate and test an adaptive algorithm where also the damping parameter of the Zarantonello iteration is adaptively adjusted. Numerical experiments underline the theoretical findings." @default.
- W4308670810 created "2022-11-14" @default.
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- W4308670810 date "2022-11-08" @default.
- W4308670810 modified "2023-10-14" @default.
- W4308670810 title "Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs" @default.
- W4308670810 doi "https://doi.org/10.48550/arxiv.2211.04123" @default.
- W4308670810 hasPublicationYear "2022" @default.
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