Weak and very weak solutions of the Laplace equation and the Stokes system with prescribed regularity

To verify theoretical results it is sometimes important to use a numerical example where the solution has a particular regularity. The paper describes one approach to construct such examples. It is based on the regularity theory for elliptic boundary value problems.

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Bibliographic Details
Published inExamples and counterexamples Vol. 8; p. 100198
Main Authors Apel, Thomas, Lorenz, Katharina, Nicaise, Serge
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2025
Elsevier
Subjects
Finite element approximation
Laplace equation
Non-homogeneous boundary conditions
Stokes system
Laplace equation
Finite element approximation
Stokes system
Non-homogeneous boundary conditions
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ISSN2666-657X
2666-657X
DOI10.1016/j.exco.2025.100198

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Summary:To verify theoretical results it is sometimes important to use a numerical example where the solution has a particular regularity. The paper describes one approach to construct such examples. It is based on the regularity theory for elliptic boundary value problems.
ISSN:2666-657X
2666-657X
DOI:10.1016/j.exco.2025.100198