  This paper focuses on the numerical solution of elliptic partial differential
equations (PDEs) with Dirichlet and mixed boundary conditions, specifically
addressing the challenges arising from irregular domains. Both finite element
method (FEM) and finite difference method (FDM), face difficulties in dealing
with arbitrary domains. The paper introduces a novel nodal symmetric ghost
finite element method approach, which combines the advantages of FEM and FDM.
The method employs bilinear finite elements on a structured mesh, and provides
a detailed implementation description. A rigorous a priori convergence rate
analysis is also presented. The convergence rates are validated with many
numerical experiments, in both one and two space dimensions.
