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- W3011245541 abstract "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 textcolor[rgb]{0.00,0.00,1.00}{$L_2$-error estimate} of $O(h^{k+frac{1}{2}})$-order for the discrete solution when the $k$th-order polynomials are used for $kgeq 0$. Moreover, for a special class of meshes, we also obtain the textcolor[rgb]{0.00,0.00,1.00}{optimal error} estimate of $O(h^{k+1})$-order in the $L_2$-norm. A derivative recovery formula is presented to approximate the convection textcolor[rgb]{1.00,0.00,0.00}{directional 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." @default.
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- W3011245541 date "2020-06-01" @default.
- W3011245541 modified "2023-09-23" @default.
- W3011245541 title "The weak Galerkin finite element method for the transport-reaction equation" @default.
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- W3011245541 doi "https://doi.org/10.1016/j.jcp.2020.109399" @default.
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