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The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …

We describe, in the framework of steady-state diffusion problems, the history of the
development of the so-called hybridizable discontinuous Galerkin (HDG) methods, since …

This book introduces the basic ideas to build discontinuous Galerkin methods and, at the
same time, incorporates several recent mathematical developments. The presentation is to a …

Originally introduced in [146, 158], Hybrid High-Order (HHO) methods provide a framework
for the discretisation of models based on Partial Differential Equations (PDEs) with features …

We consider the discretization of a boundary value problem for a general linear second-
order elliptic operator with smooth coefficients using the Virtual Element approach. As in [AH …

This paper introduces a finite element method by using a weakly defined gradient operator
over generalized functions. The use of weak gradients and their approximations results in a …

We devise an arbitrary-order locking-free method for linear elasticity. The method relies on a
pure-displacement (primal) formulation and leads to a symmetric, positive definite system …

A new weak Galerkin (WG) method is introduced and analyzed for the second order elliptic
equation formulated as a system of two first order linear equations. This method, called WG …

An hp-version interior penalty discontinuous Galerkin method (DGFEM) for the numerical
solution of second-order elliptic partial differential equations on general computational …