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Titlebook: Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential ; Gabriel R. Barrenechea,Franco Brezzi

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Static Condensation, Hybridization, and the Devising of the HDG Methods,mework of steady-state diffusion problems. We begin by revisiting the classic techniques of . of continuous finite element methods and that of . of mixed methods, and show that they can be reinterpreted as discrete versions of a characterization of the associated exact solution in terms of solutions
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A Survey of Trefftz Methods for the Helmholtz Equation, particularly popular for time-harmonic wave problems, as their trial spaces contain oscillating basis functions and may achieve better approximation properties than classical piecewise-polynomial spaces. We review the construction and properties of several Trefftz variational formulations developed
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Discretization of Mixed Formulations of Elliptic Problems on Polyhedral Meshes,r mixed formulations of elliptic problems. For a class of low-order mixed-hybrid schemes, we show connections between these principles and prove that the consistency and stability conditions must lead to a member of the mimetic family of schemes regardless of the selected discretization framework. F
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Virtual Element Implementation for General Elliptic Equations,In the present paper we detail the implementation of the Virtual Element Method for two dimensional elliptic equations in primal and mixed form with variable coefficients.
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