Curved elements in weak Galerkin finite element methods

A weak Galerkin finite element method is devised for the Poisson equation with Dirichlet boundary value when curved elements are employed in the numerical scheme. Optimal order error estimates are derived for the weak Galerkin solution in both the H1-norm and the L2-norm. Numerical results are produced to demonstrate the performance of the weak Galerkin method on general curved partitions.