A Relaxed Kačanov Iteration for the $p$-Poisson Problem

Diening L, Fornasier M, Wank M (2017)
arXiv:1702.03844.

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In this paper, we introduce an iterative linearization scheme that allows to approximate the weak solution of the $p$-Poisson problem \begin{align*} -\operatorname{div}(|\nabla u|^{p-2}\nabla u) &= f\quad\text{in }\Omega, u&= 0\quad\text{on}\partial\Omega \end{align*} for $1 < p \leq 2$. The algorithm can be interpreted as a relaxed Ka\v{c}anov iteration. We prove that the algorithm converges at least with an algebraic rate.
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Diening L, Fornasier M, Wank M. A Relaxed Kačanov Iteration for the $p$-Poisson Problem. arXiv:1702.03844. 2017.
Diening, L., Fornasier, M., & Wank, M. (2017). A Relaxed Kačanov Iteration for the $p$-Poisson Problem. arXiv:1702.03844
Diening, L., Fornasier, M., and Wank, M. (2017). A Relaxed Kačanov Iteration for the $p$-Poisson Problem. arXiv:1702.03844.
Diening, L., Fornasier, M., & Wank, M., 2017. A Relaxed Kačanov Iteration for the $p$-Poisson Problem. arXiv:1702.03844.
L. Diening, M. Fornasier, and M. Wank, “A Relaxed Kačanov Iteration for the $p$-Poisson Problem”, arXiv:1702.03844, 2017.
Diening, L., Fornasier, M., Wank, M.: A Relaxed Kačanov Iteration for the $p$-Poisson Problem. arXiv:1702.03844. (2017).
Diening, Lars, Fornasier, Massimo, and Wank, Maximilian. “A Relaxed Kačanov Iteration for the $p$-Poisson Problem”. arXiv:1702.03844 (2017).
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