Abstract
The div—curl system is an important class of first-order partial differential equations. This system governs, for example, static electromagnetic fields, and incompressible irrotational fluid flows. The div—curl system is also fundamental from a theoretical point of view, since the Stokes equations and the incompressible Navier—Stokes equations written in the first-order velocity—pressure—vorticity formulation, as well as the Maxwell equations consist of two div—curl systems. The three-dimensional div—curl system is traditionally considered as “overdetermined” or “overspecified”, because it has four equations involving only three unknowns. For this reason, it is not easy to solve by using conventional numerical methods. In this chapter, we will prove that the div—curl system is really well determined and strongly elliptic by introducing a dummy variable, and explain that for the well-posedness the div—curl system should have two algebraic boundary conditions. We will also show that the LSFEM is the best choice for numerical solution of the div—curl system.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Jiang, Bn. (1998). Div—Curl System. In: The Least-Squares Finite Element Method. Scientific Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03740-9_5
Download citation
DOI: https://doi.org/10.1007/978-3-662-03740-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08367-9
Online ISBN: 978-3-662-03740-9
eBook Packages: Springer Book Archive