Neumann boundary conditions in potential theory

E458005

boundary condition type mathematical concept partial differential equation boundary condition

Neumann boundary conditions in potential theory specify that the normal derivative of a potential function on a boundary is prescribed, modeling situations where flux across the boundary is controlled rather than the potential itself.

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Observed surface forms (3)

Surface form	Occurrences
Neumann boundary condition	2
Neumann boundary condition at finite distance	1
Neumann boundary conditions	1

Statements (49)

Predicate	Object
instanceOf	boundary condition type ⓘ mathematical concept ⓘ partial differential equation boundary condition ⓘ
affects	uniqueness of solutions to potential problems ⓘ
appliesTo	Laplace equation NERFINISHED ⓘ Poisson equation NERFINISHED ⓘ harmonic functions ⓘ
assumes	boundary with sufficient smoothness ⓘ
category	homogeneous Neumann boundary conditions ⓘ inhomogeneous Neumann boundary conditions ⓘ
contrastsWith	Dirichlet boundary conditions in potential theory ⓘ Robin boundary conditions in potential theory ⓘ
controls	flux across the boundary ⓘ
ensures	conservation of total flux across boundary ⓘ
field	applied mathematics ⓘ mathematical physics ⓘ potential theory ⓘ
homogeneousForm	∂u/∂n = 0 on the boundary ⓘ
implies	solution is determined up to an additive constant ⓘ
involves	normal derivative of the potential function ⓘ outward unit normal vector to the boundary ⓘ
isPartOf	classical boundary value problem theory ⓘ
mathematicalForm	∂u/∂n = g on the boundary ⓘ
models	impermeable wall in diffusion problems ⓘ perfectly insulated surface in heat flow ⓘ perfectly insulating boundary in electrostatics ⓘ
namedAfter	Carl Neumann NERFINISHED ⓘ
relatedTo	Green's functions with Neumann boundary data ⓘ Green's identities NERFINISHED ⓘ Robin (mixed) boundary conditions NERFINISHED ⓘ boundary integral equations ⓘ mixed boundary conditions ⓘ
requires	compatibility condition on total flux for existence of solution ⓘ fixing reference potential to ensure uniqueness ⓘ
specifies	normal derivative of a potential on a boundary ⓘ
usedFor	modeling insulated boundaries ⓘ modeling no-flux boundaries ⓘ modeling prescribed flux boundaries ⓘ
usedIn	boundary element methods ⓘ boundary value problems ⓘ electrostatics ⓘ finite difference methods ⓘ finite element methods ⓘ fluid flow ⓘ gravitation theory ⓘ heat conduction ⓘ steady-state diffusion models ⓘ variational formulations of PDEs ⓘ
usedToDetermine	normal component of gradient on boundary ⓘ

Referenced by (5)

Full triples — surface form annotated when it differs from this entity's canonical label.

Franz Ernst Neumann → notableWork → Neumann boundary conditions in potential theory ⓘ

Laplace equation → typicalBoundaryCondition → Neumann boundary conditions in potential theory ⓘ

this entity surface form: Neumann boundary condition

Laplace operator → relatedConcept → Neumann boundary conditions in potential theory ⓘ

this entity surface form: Neumann boundary condition

Sommerfeld radiation condition → contrastsWith → Neumann boundary conditions in potential theory ⓘ

this entity surface form: Neumann boundary condition at finite distance

Laplacian spectrum → relatedTo → Neumann boundary conditions in potential theory ⓘ

this entity surface form: Neumann boundary conditions