# Plain convergence of adaptive algorithms without exploiting reliability and efficiency

@article{Gantner2020PlainCO, title={Plain convergence of adaptive algorithms without exploiting reliability and efficiency}, author={Gregor Gantner and Dirk Praetorius}, journal={ArXiv}, year={2020}, volume={abs/2009.01349} }

We consider $h$-adaptive algorithms in the context of the finite element method and the boundary element method. Under quite general assumptions on the building blocks SOLVE, ESTIMATE, MARK and REFINE of such algorithms we prove plain convergence in the sense that the adaptive algorithm drives the underlying a posteriori error estimator to zero. Unlike available results in the literature, our analysis avoids the use of any reliability and efficiency estimate but relies only on structural…

## 2 Citations

### Plain convergence of goal-oriented adaptive FEM

- MathematicsArXiv
- 2022

We discuss goal-oriented adaptivity in the frame of conforming finite element methods and plain convergence of the related a posteriori error estimator for different general marking strategies. We…

### Adaptive Quasi-Monte Carlo Finite Element Methods for Parametric Elliptic PDEs

- Computer Science, MathematicsJournal of Scientific Computing
- 2022

A class of deterministic quasi-Monte Carlo integration rules derived from Polynomial lattices is performed that allows to control a-posteriori the integration error without querying the governing PDE and does not incur the curse of dimensionality.

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