Article ID Journal Published Year Pages File Type
471085 Computers & Mathematics with Applications 2014 10 Pages PDF
Abstract

This paper introduces a novel lowest-order discontinuous Petrov–Galerkin (dPG) finite element method (FEM) for the Poisson model problem. The ultra-weak formulation allows for piecewise constant and affine ansatz functions and for piecewise affine and lowest-order Raviart–Thomas test functions. This lowest-order discretization for the Poisson model problem allows for a direct proof of the discrete inf–sup condition and a complete a priori and a posteriori error analysis. Numerical experiments investigate the performance of the method and underline the quasi-optimal convergence.

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