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.
Original language | English |
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Pages (from-to) | 1503-1512 |
Number of pages | 10 |
Journal | Computers and mathematics with applications |
Volume | 68 |
Issue number | 11 |
DOIs | |
Publication status | Published - 2014 |
Externally published | Yes |