Dirichlet boundary conditions

E466250

boundary condition concept in partial differential equations mathematical concept

Dirichlet boundary conditions are a fundamental type of boundary condition in differential equations and mathematical physics, specifying the values that a solution must take on the boundary of the domain.

Try in SPARQL Jump to: Surface forms Statements Referenced by

Observed surface forms (2)

Surface form	Occurrences
Dirichlet boundary condition	3
Dirichlet boundary condition at finite distance	1

Statements (47)

Predicate	Object
instanceOf	boundary condition ⓘ concept in partial differential equations ⓘ mathematical concept ⓘ
appliesTo	elliptic partial differential equations ⓘ hyperbolic partial differential equations ⓘ parabolic partial differential equations ⓘ
assumes	boundary values are known a priori ⓘ
category	deterministic boundary conditions ⓘ
contrastedWith	Neumann boundary conditions NERFINISHED ⓘ Robin boundary conditions ⓘ
defines	values of a solution on the boundary of a domain ⓘ
domain	boundary of the spatial domain ⓘ
field	applied mathematics ⓘ engineering ⓘ mathematical physics ⓘ numerical analysis ⓘ partial differential equations ⓘ
historicalPeriod	19th century mathematics ⓘ
homogeneousForm	u(x)=0 on the boundary ⓘ
mathematicalForm	u(x)=g(x) for x on the boundary ⓘ
namedAfter	Johann Peter Gustav Lejeune Dirichlet NERFINISHED ⓘ
property	can be non-homogeneous ⓘ can be space-dependent ⓘ can be time-dependent ⓘ
relatedConcept	Dirichlet problem NERFINISHED ⓘ boundary value problem ⓘ
role	ensure uniqueness of solutions under suitable conditions ⓘ make boundary value problems well-posed ⓘ
specialCase	homogeneous Dirichlet boundary conditions ⓘ
specifies	solution values rather than derivatives ⓘ
usedFor	modeling fixed displacement in elasticity ⓘ modeling fixed potential in electrostatics ⓘ modeling fixed temperature on a boundary ⓘ modeling prescribed concentration in diffusion problems ⓘ
usedIn	Laplace equation NERFINISHED ⓘ Poisson equation NERFINISHED ⓘ Schrödinger equation NERFINISHED ⓘ boundary element methods ⓘ electrostatics ⓘ finite difference methods ⓘ finite element methods ⓘ finite volume methods ⓘ fluid dynamics ⓘ heat equation ⓘ steady-state heat conduction ⓘ structural mechanics ⓘ wave equation ⓘ

Referenced by (6)

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

Peter Gustav Lejeune Dirichlet → notableWork → Dirichlet boundary conditions ⓘ

Laplace equation → typicalBoundaryCondition → Dirichlet boundary conditions ⓘ

this entity surface form: Dirichlet boundary condition

Laplace operator → relatedConcept → Dirichlet boundary conditions ⓘ

this entity surface form: Dirichlet boundary condition

Sommerfeld radiation condition → contrastsWith → Dirichlet boundary conditions ⓘ

this entity surface form: Dirichlet boundary condition at finite distance

Laplacian spectrum → relatedTo → Dirichlet boundary conditions ⓘ

Sobolev spaces → relatedConcept → Dirichlet boundary conditions ⓘ

this entity surface form: Dirichlet boundary condition