Convergence and optimality of an adaptive modified weak Galerkin finite element method

An adaptive modified weak Galerkin method (AmWG) for an elliptic problem is studied in this paper, addition to its convergence and optimality. The bilinear form simplified without the need of skeletal variable, approximation space chosen as discontinuous polynomial method. Upon a reliable residual-based posteriori error estimator, algorithm proposed together with quasi-optimality proved lowest order case. primary tool bridge connection between Crouzeix-Raviart nonconforming finite element. Unlike traditional analysis methods space, AmWG penalty parameter free. Numerical results are presented support theoretical results.