The Weak Galerkin Finite Element Method for the Transport-Reaction Equation
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We present and analyze a weak Galerkin finite element method for solving the transport-reaction equation in d space dimensions. This method is highly flexible by allowing the use of discontinuous finite element on general meshes consisting of arbitrary polygon/polyhedra. We derive the [rgb]0.00,0.00,1.00L_2-error estimate of O(h^k+1/2)-order for the discrete solution when the kth-order polynomials are used for k≥ 0. Moreover, for a special class of meshes, we also obtain the [rgb]0.00,0.00,1.00optimal error estimate of O(h^k+1)-order in the L_2-norm. A derivative recovery formula is presented to approximate the convection [rgb]1.00,0.00,0.00directional derivative and the corresponding superconvergence estimate is given. Numerical examples on compatible and non-compatible meshes are provided to show the effectiveness of this weak Galerkin method.
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