Finite Element Fictitious Domain Method for Elliptic PDEs Over Curved‐Complex Domains

ABSTRACT This study uses a simple uniform Cartesian mesh and finite element method with a penalty approach to decipher elliptic PDEs defined over curved‐complex domains, irrespective of the boundary trajectory. The convergence of the solution of the penalized problem to the original solution is equipped with the discrete error estimates in the and norms in terms of the penalty parameter and mesh size . Numerical investigations performed on different types of domain confirm the applicability and efficiency of the proposed method and validate the theoretical results.