Dirichlet Boundary Condition

A specification that a function or field takes prescribed values on the boundary of a spatial domain; in boundary value problems this fixes the trace of the solution on the domain's boundary.

A boundary condition that prescribes the value of the unknown solution itself on the boundary of the domain (the trace of the function is fixed on ∂Ω).

A boundary condition that prescribes the exact value of a primary dependent variable (e.g., displacement, temperature, electric potential) at each point of a portion of the domain boundary, enforced pointwise in strong formulations or via suitable numerical enforcement strategies in discrete approximations.