Neumann boundary conditions

Neumann boundary conditions specify that the rate of change or gradient of a function (such as temperature or pressure) across a boundary is fixed, often set to zero. Essentially, they control how a quantity flows across the boundary rather than its absolute value there. For example, in heat transfer, a Neumann condition might mean no heat enters or leaves the boundary, indicating an insulated edge. These conditions are used in mathematical models to describe situations where the flux or flow across boundaries is known, allowing for accurate solutions of differential equations governing physical phenomena.