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We propose two different discrete formulations for the weak imposition of the Neumann boundary conditions of the Darcy flow. The Raviart-Thomas mixed finite element on both triangular and quadrilateral meshes is considered for both methods. One is a consis ...
Standard high order Galerkin methods, such as pure spectral or high order finite element methods, have insufficient stability properties when applied to transport dominated problems. In this paper we review some stabilization strategies for pure spectral m ...
In this paper we present the continuous and discontinuous Galerkin methods in a unified setting for the numerical approximation of the transport dominated advection-reaction equation. Both methods are stabilized by the interior penalty method, more precise ...
In this paper we give an analysis of a bubble stabilized discontinuous Galerkin method (BSDG) for elliptic and parabolic problems. The method consists of stabilizing the numerical scheme by enriching the discontinuous finite element space elementwise by qua ...
We consider a discontinuous Galerkin finite element method for the advection– reaction equation in two space–dimensions. For polynomial approximation spaces of degree greater than or equal to two on triangles we propose a method where stability is obtained ...
We consider DG-methods for 2nd order scalar elliptic problems using piecewise affine approximation in two or three space dimensions. We prove that both the symmetric and the non-symmetric version of the DG-method have regular system matrices also without pen ...
In this study, we consider some recent stabilization techniques for the Stokes' problem and show that they are instances of the framework proposed by Brezzi and Fortin in "A minimal stabilisation procedure for mixed finite element methods" (Numer Math 89, ...
In this Note we prove that in two and three space dimensions, the symmetric and non-symmetric discontinuous Galerkin method for second order elliptic problems is stable when using piecewise linear elements enriched with quadratic bubbles without any penali ...
We extend the results on minimal stabilization of Burman and Stamm[J. Sci. Comp., 33 (2007), pp. 183-208] to the case of the local discontinuous Galerkin methods on mixed form. The penalization term on the faces is relaxed to act only on a part of the poly ...
We propose a stabilized mixed finite element method based on the Scott-Vogelius element tor the Oseen equation. Here. only convection has to he stabilized since by construction both the discrete pressure and the divergence of the discrete velocities, are c ...
