Volume 52, pp. 455-479, 2020.

An a-priori error analysis for discontinuous Lagrangian finite elements applied to nonconforming dual-mixed formulations: Poisson and Stokes problems

Tomás P. Barrios and Rommel Bustinza


In this paper, we discuss the well-posedness of a mixed discontinuous Galerkin (DG) scheme for the Poisson and Stokes problems in 2D, considering only piecewise Lagrangian finite elements. The complication here lies in the fact that the classical Babuška-Brezzi theory is difficult to verify for low-order finite elements, so we proceed in a non-standard way. First, we prove uniqueness, and then we apply a discrete version of Fredholm's alternative theorem to ensure existence. The a-priori error analysis is done by introducing suitable projections of the exact solution. As a result, we prove that the method is convergent, and, under standard additional regularity assumptions on the exact solution, the optimal rate of convergence of the method is guaranteed.

Full Text (PDF) [410 KB], BibTeX

Key words

discontinuous Galerkin, Lagrange shape functions, a-priori error estimates

AMS subject classifications

65N30; 65N12; 65N15

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