Question

Distingnish between essential boundry condition and natural boundary condition

Answer 1

Essential boundary conditions are conditions that are imposed explicitly on the solution and natural boundary conditions are those that automatically will be satisfied after solution of the problem. In the case of Finite Element approximations, the essential conditions will be exactly satisfied but the natural conditions only up to the order of the method . In many cases, the essential conditions correspond to Dirichlet boundary conditions when the problem is written as a boundary value problem for a partial differential equation. The natural condition corresponds to a Neumann condition, a stress-free condition, or something similar, depending on the problem. However, there are cases that are not so clear cut , so to identify Dirichlet=essential and Neumann=natural is not really correct. For instance, Dirichlet conditions can be assigned as natural conditions using Nitsche’s method, and Neumann conditions can be transformed to essential conditions using so-called mixed methods.

Answer 2

Answer:

Essential or geometric boundary conditions which are imposed on the primary variable like displacements, and. Natural or force boundary conditions which are imposed on the secondary variable like forces and tractions.