@inproceedings{9101d6a6ea6f40b0894a80bacd9fe736,
title = "Quasinorms in semilinear elliptic problems",
abstract = "In this note we examine the a priori and a posteriori analysis of discontinuous Galerkin finite element discretisations of semilinear elliptic PDEs with polynomial nonlinearity. We show that optimal a priori error bounds in the energy norm are only possible for low order elements using classical a priori error analysis techniques. We make use of appropriate quasinorms that results in optimal energy norm error control. We show that, contrary to the a priori case, a standard a posteriori analysis yields optimal upper bounds and does not require the introduction of quasinorms. We also summarise extensive numerical experiments verifying the analysis presented and examining the appearance of layers in the solution.",
author = "James Jackaman and Tristan Pryer",
year = "2020",
month = aug,
day = "12",
doi = "10.1007/978-3-030-41800-7_12",
language = "English",
isbn = "9783030417994",
series = "Lecture Notes in Computational Science and Engineering",
publisher = "Springer, Singapore",
pages = "183--200",
editor = "Barrenechea, {Gabriel R.} and John Mackenzie",
booktitle = "Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2018",
address = "Singapore",
note = "International Conference on Boundary and Interior Layers, BAIL 2018 ; Conference date: 18-06-2018 Through 22-06-2018",
}