hp-Adaptive Iterative Linearization Discontinuous-Galerkin FEM for Quasilinear Elliptic Boundary Value Problems

HOUSTON, PAUL; WIHLER, THOMAS

Abstract

In this article we consider the a posteriori error analysis of hp-version discontinuous Galerkin finite element methods for the numerical solution of a second-order quasilinear elliptic boundary value problem of strongly monotone type. In particular, we employ and analyze a practical solution scheme based on exploiting a discrete Kačanov iterative linearization. The resulting a posteriori error bound explicitly takes into account the three sources of error: discretization, linearization, and linear solver errors. Numerical experiments are presented to demonstrate the practical performance of the proposed hp-adaptive refinement strategy.

Citation

HOUSTON, P., & WIHLER, T. (2020). hp-Adaptive Iterative Linearization Discontinuous-Galerkin FEM for Quasilinear Elliptic Boundary Value Problems. In S. Sherwin, D. Moxey, J. Peiro, P. Vincent, & C. Schwab (Eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 (407–417). https://doi.org/10.1007/978-3-030-39647-3

• Conference Name: Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018
• Conference Location: London, UK
• Start Date: Jul 9, 2018
• End Date: Jul 13, 2018
• Acceptance Date: Aug 16, 2019
• Online Publication Date: Mar 9, 2020
• Publication Date: 2020
• Deposit Date: Mar 5, 2020
• Publicly Available Date: Mar 10, 2021
• Pages: 407–417
• Series Title: Lecture Notes in Computational Science and Engineering
• Series Number: 134
• Series ISSN: 1439-7358
• Book Title: Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018
• ISBN: 9783030396466
• DOI: https://doi.org/10.1007/978-3-030-39647-3
• Public URL: https://nottingham-repository.worktribe.com/output/4094305
• Publisher URL: https://www.springer.com/gp/book/9783030396466
• Related Public URLs: http://www.icosahom2018.org/