Dirichlet Boundary Conditions

Dirichlet boundary conditions specify the exact values a solution must take on the boundary of a region. Imagine solving a heat distribution problem: setting a fixed temperature along the edges of a metal plate means the temperature at those edges is known and maintained. These conditions "pin down" the solution at the boundary, ensuring the problem is well-defined. They are often used in physical and mathematical models where boundary values are controlled or known in advance.