Partial differential equations

• How to Solve Poisson’s Equation with Robin Boundary Conditions
  Learn how Robin boundary conditions enter Poisson’s equation, derive the weak form, and check existence and uniqueness with a worked example.
• How Do the Two Dirichlet Laplacian Operators Differ?
  The first Dirichlet Laplacian is a bounded weak operator into H⁻¹; the second is its stronger L² realization on H² functions.
• What Is the 9-Point Finite-Difference Stencil for the Laplacian?
  The standard 2D 9-point Laplacian uses center, axial, and diagonal grid values with weights −20, 4, and 1, divided by 6h².