Quasinorms in semilinear elliptic problems

James Jackaman, Tristan Pryer

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish
Title of host publicationBoundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2018
EditorsGabriel R. Barrenechea, John Mackenzie
PublisherSpringer, Singapore
Pages183-200
Number of pages18
ISBN (Print)9783030417994
DOIs
Publication statusE-pub ahead of print - 12 Aug 2020
EventInternational Conference on Boundary and Interior Layers, BAIL 2018 - Glasgow, UK United Kingdom
Duration: 18 Jun 201822 Jun 2018

Publication series

NameLecture Notes in Computational Science and Engineering
Volume135
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

ConferenceInternational Conference on Boundary and Interior Layers, BAIL 2018
CountryUK United Kingdom
CityGlasgow
Period18/06/1822/06/18

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering(all)
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics

Cite this

Jackaman, J., & Pryer, T. (2020). Quasinorms in semilinear elliptic problems. In G. R. Barrenechea, & J. Mackenzie (Eds.), Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2018 (pp. 183-200). (Lecture Notes in Computational Science and Engineering; Vol. 135). Springer, Singapore. https://doi.org/10.1007/978-3-030-41800-7_12