Quasinorms in semilinear elliptic problems

James Jackaman, Tristan Pryer

Research output: Chapter or section in a book/report/conference proceedingChapter in a published conference proceeding

1 Citation (SciVal)


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
Number of pages18
ISBN (Print)9783030417994
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
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100


ConferenceInternational Conference on Boundary and Interior Layers, BAIL 2018
Country/TerritoryUK United Kingdom

ASJC Scopus subject areas

  • Modelling and Simulation
  • General Engineering
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics


Dive into the research topics of 'Quasinorms in semilinear elliptic problems'. Together they form a unique fingerprint.

Cite this