Skip to content

Boundary conditions and loads

Boundary conditions specify the behavior of a problem’s solution on the boundaries of the computational domain. They are essential for correctly formulating and solving partial differential equations using the finite element method. In broad terms, boundary conditions are usually classified into:

  • Essential (Dirichlet) Boundary Conditions:

    These conditions prescribe the value of the solution itself on the boundary. For instance, in a structural problem, a Dirichlet boundary condition might fix displacements of a beam’s endpoints to zero. In a thermal problem, it could fix the temperature at the boundary to a known value.

  • Natural (Neumann) Boundary Conditions:

    These conditions specify the value of the derivative of the solution normal to the boundary or, in many physical problems, the flux (such as heat flux, fluid flux, or stress). In a structural context, this may correspond to prescribing surface tractions rather than displacements. In a thermal problem, it can represent a specified heat flow across the boundary.

  • Others:

    Other options to apply loading or constraints include the definition of body forces, mass points or spring-damper elements.

Essential (Dirichlet) Boundary Conditions

Natural (Neumann) Boundary Conditions

Others