A weak Galerkin mixed finite element method for second order elliptic problems

By Junping Wang, Xiu Ye. Mathematics of Computation, 2012

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Virtual Element Methods for general second order elliptic problems on polygonal meshes (2014, unknown): “See [22], [30], [31], [32], , [33], [35], [36], [37], [39], [55], [54], [56], [68], [69].”
Weak Galerkin method for the coupled Darcy-Stokes flow (2014, methodology): “Optimal order of a priori error estimates has been observed and established for various weak Galerkin discretization schemes for second order elliptic equations [39, 40, 31].”
A weak Galerkin finite element method for the stokes equations (2013, methodology): “A proof of the lemma can be found in [16], which is based on some technical inequalities for functions defined on polygon/polyhedral elements with shape regularity.”
Robust Globally Divergence-Free Weak Galerkin Methods for Stokes Equations (2016, methodology): “([64]) For all qh = {qhi, qhb} ∈ Qh, T ∈ Th, the relation ∇w,kqh = 0 holds true on T if and only if qhi = qhb = constant.”
A Posteriori Error Estimates for the Weak Galerkin Finite Element Methods on Polytopal Meshes (2019, methodology): “Let Th be a partition of the domain Ω consisting of polygons in two dimensions or polyhedra in three dimensions satisfying a set of conditions specified in [25].”
A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation (2013, methodology): “The mixed weak Galerkin ﬁnite element method is studied in [34].”