Bounds and regularity of Solutions of Planar Div-curl Problems
Giles Auchmuty
TL;DR
This paper establishes new 2-norm bounds and regularity results for solutions to planar div-curl boundary value problems, utilizing harmonic decomposition to separate source and boundary effects.
Contribution
It introduces novel bounds for solutions of planar div-curl problems with various boundary conditions, enhancing understanding of solution regularity and boundary influence.
Findings
Derived new 2-norm bounds for solutions
Separated source and boundary effects via harmonic decomposition
Provided regularity estimates for solutions
Abstract
New 2-norm bounds for solutions of planar div-curl boundary value problems on bounded planar regions are described. Prescribed flux, tangential trace and mixed boundary boundary are treated. A harmonic decomposition is used to separate components of the solution due to source terms from the components due to boundary data. Estimates for the solutions are obtained and some regularity results are described
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Contact Mechanics and Variational Inequalities · Numerical methods in engineering