The first boundary condition: the numerical value of the unknown function on the boundary is given;

The second boundary condition: the directional derivative of the normal outside the boundary of the unknown function is given;

The third boundary condition: the linear combination of the function value of the unknown function and the derivative of the outer normal direction on the given boundary.

The initial condition refers to the initial state of the process, that is, the value of the unknown function and its partial derivative to time at the initial time t=0. In finite element, many initial conditions must be given in advance. Different field equations correspond to different initial conditions. In short, in order to determine the solution of the universal equation, we must provide enough initial conditions and boundary conditions!

Boundary condition refers to solving the variation law of variables or their derivatives on regional boundaries with time and place. The boundary condition is the premise of the definite solution of the governing equation, and any problem needs to be given the boundary condition. The treatment of boundary conditions directly affects the accuracy of calculation results. In order to solve differential equations with definite solutions, conditions must be introduced. These additional conditions are called definite solution conditions.

Neumann boundary conditions In mathematics, Neumann boundary conditions are also called "second boundary conditions" of ordinary differential equations or partial differential equations. Neumann boundary conditions specify the differentiation of solutions of differential equations on the boundary.