The finite element method with penalty

Key Points

• The penalized finite element method effectively solves the Poisson equation with boundary conditions, demonstrating notable convergence rates.
• Key evidence showed significant improvements in convergence when applying the penalty method on a model Poisson equation.
• Analysis involved applying the penalty method to derive solutions for the Poisson equation while relaxing traditional boundary conditions efficiently and effectively. Higher convergence rates were achieved when non-boundary satisfying functions were utilized.