Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2014-23

C. Carstensen, D. Gallistl, F. Hellwig, L. Weggler


Low-Order dPG-FEM for an Elliptic PDE


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 ane ansatz functions and for piecewise ane 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.


Keywords: FEM, discontinuous, Petrov-Galerkin, DPG, Poisson
2010 MSC: 65N30


Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2014-23


11 pp.