Journal ArticleDOI
Optimality of an adaptive finite element method for the p-Laplacian equation
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This article is published in Ima Journal of Numerical Analysis.The article was published on 2012-04-01. It has received 91 citations till now. The article focuses on the topics: Mixed finite element method & Extended finite element method.read more
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Axioms of adaptivity
TL;DR: In this paper, efficiency exclusively characterizes the approximation classes involved in terms of the best-approximation error and data resolution and so the upper bound on the optimal marking parameters does not depend on the efficiency constant.
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Adaptive Inexact Newton Methods with A Posteriori Stopping Criteria for Nonlinear Diffusion PDEs
Alexandre Ern,Martin Vohralík +1 more
TL;DR: The efficiency and robustness of the estimates with respect to the size of the nonlinearity owing to the error measure involving the dual norm of the residual are proved and a guaranteed upper bound on the overall error is yielded.
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Adaptive FEM with Optimal Convergence Rates for a Certain Class of Nonsymmetric and Possibly Nonlinear Problems
TL;DR: This work analyzes adaptive mesh-refining algorithms for conforming finite element discretizations of certain nonlinear second-order partial differential equations and proves convergence even with optimal algebraic convergence rates.
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BMO estimates for the p-Laplacian
TL;DR: In this article, it was shown that f ∈ BMO implies that A ( ∇ u ) inherits the Campanato and VMO regularity of f, which is the limiting case of the nonlinear Calderon-Zygmund theory.
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Quasi-optimal convergence rate for an adaptive boundary element method
TL;DR: It is proved that adaptive mesh refinement is superior to uniform mesh refinement and convergence of an $h$-adaptive algorithm that is driven by a weighted residual error estimator.