Numerical techniques have revolutionized the field of solving partial differential equations (PDEs), especially when dealing with irregular geometries. This study aims to explore various numerical methods for solving PDEs in irregular geometries and compare their efficiency and approximate. The research focuses on finite element methods (FEM) and finite volume methods (FVM), analyzing their application and limitations in such scenarios. The results highlight the importance of selecting appropriate numerical methods based on the nature of the problem and the geometry involved, offering valuable insights for future research and practical applications.