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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
A finite element method for Burgers' equation is studied. The method is analyzed using techniques from stabilized finite element methods and convergence to entropy solutions is proven under certain hypotheses on the artificial viscosity. In particular we a ...
We use the lowest possible approximation order, piecewise linear, continuous velocities and piecewise constant pressures to compute solutions to Stokes equation and Darcy's equation, applying an edge stabilization term to avoid locking. We prove that the f ...
In this Note we propose a stabilized explicit coupling scheme for fluid-structure interaction based on Nitsche's method. The scheme is stable irrespective of the fluid-solid density ratio. Numerical experiments show that optimal time accuracy can be obtain ...
In this Note we prove that in one space dimension, the symmetric discontinuous Galerkin method for second order elliptic problems is stable for polynomial orders p≥2 without using any stabilization parameter. The method yields optimal convergence rat ...
A continuous interior penalty hp-finite element method that penalizes the jump of the discrete solution across mesh interfaces is introduced. Error estimates are obtained for first-order and advection-dominated transport operators. The analysis relies on t ...
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 ...
In this note we introduce and analyze a stabilized finite element method for the generalized Stokes equation. Stability is obtained by adding a least squares penalization of the gradient jumps across element boundaries. The method can be seen as a higher o ...
We propose to apply the recently introduced local projection stabilization to the numerical computation of the Oseen equation at high Reynolds number. The discretization is done by nested finite element spaces. Using a priori error estimation techniques, w ...
