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An Anisotropic Recovery-Based Error Estimator for Adaptive Discontinuous Galerkin Methods

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Abstract

We present a new recovery-based anisotropic error estimator for discontinuous Galerkin finite element approximations of advection-diffusion problems. We propose a metric-based algorithm for mesh adaptation which is driven by this error estimator. Numerical verification on several test cases, both in the steady and in the unsteady setting, shows the effectiveness of the algorithm in capturing the intrinsic directionalities of the solution.

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Acknowledgements

We would like to acknowledge Mario Allora who carried out the first numerical assessments in [1] under the supervision of the three authors. The financial support of INdAM-GNCS Projects 2020 is gratefully acknowledged by Simona Perotto. Nicola Ferro thanks Fondazione Fratelli Confalonieri and Istituto Nazionale di Alta Matematica (INdAM) for the awarded grants. Andrea Cangiani was supported by the UK Medical Research Council (MRC), Grant No. MR/T017988/1.

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Authors and Affiliations

  1. MOX – Dipartimento di Matematica Politecnico di Milano, Piazza L. da Vinci, 32, 20133, Milano, Italy

    Nicola Ferro & Simona Perotto

  2. Scuola Internazionale Superiore di Studi Avanzati - SISSA, Via Bonomea, 265, 34136, Trieste, Italy

    Andrea Cangiani

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  1. Nicola Ferro
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Correspondence to Nicola Ferro.

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Ferro, N., Perotto, S. & Cangiani, A. An Anisotropic Recovery-Based Error Estimator for Adaptive Discontinuous Galerkin Methods. J Sci Comput 90, 45 (2022). https://doi.org/10.1007/s10915-021-01724-4

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