In this article an unfitted Discontinuous Galerkin Method is proposed to discretize elliptic interface problems. The method is based on the Symmetric Interior Penalty Discontinuous Galerkin Method and can also be interpreted as a generalization of the method given in [A. Hansbo, P. Hansbo, An unfitted finite element method based on Nitsche’s method for elliptic interface problems, Comp. Meth. A...

Edge-oriented stabilization methods in the framework of discontinuous Galerkin approaches have been recently proposed by Brenner [3] and particularly by Hansbo and Larson [5] for nonconforming finite element discretizations to satisfy a discrete Korn’s inequality. We develop and analyse corresponding multigrid components in combination with local Pressure-Schur-Complement methods and give numer...

We obtain a posteriori error estimates for a variant of (non-locking) stabilized nonconforming methods based on the Crouzeix-Raviart element introduced by P. Hansbo and M. G. Larson in [M2AN 37 (2003) 63-72]. We derive upper and lower a posteriori error bounds which are robust with respect to the nearly incompressible materials.

In the past decade, a combination of unfitted finite elements (or XFEM) with the Nitsche method has become a popular discretization method for elliptic interface problems. This development started with the introduction and analysis of this Nitsche-XFEM technique in the paper [A. Hansbo, P. Hansbo, Comput. Methods Appl. Mech. Engrg. 191 (2002)]. In general, the resulting linear systems have very...

We consider an unsteady convection diffusion equation which models the transport of a dissolved species in two-phase incompressible flow problems. The so-called Henry interface condition leads to a jump condition for the concentration at the interface between the two phases. In [A. Hansbo, P. Hansbo, Comput. Methods Appl. Mech. Engrg. 191 (20002)], for the purely elliptic stationary case, exten...

We present a discontinuous Galerkin method for the plate problem. The method employs a discontinuous approximation space allowing, non matching grids and diierent types of approximation spaces. Continuity is enforced weakly through the vari-ational form. Discrete approximations of the normal and twisting moments and the transversal force, which satisfy the equilibrium condition on an element le...

We present two kinds of lowest-order virtual element methods for planar linear elasticity problems. For the first one we use nonconforming method with a stabilizing term. It can be interpreted as modification Crouzeix–Raviart finite suggested in Hansbo and Larson (2003) to method. second conforming component displacement vector other. This approach seen an extension idea Kouhia Stenberg (1995) ...

Adopting the non-Darcy flow presented by Hansbo and considering nonlinear compression permeability characteristics of soils, one-dimensional consolidation problem soft clays is investigated means a continuous drainage boundary. The numerical solutions average degrees defined settlement excess pore water pressure are derived using finite difference method, correctness these verified comparing th...

one of the simplest numerical integration method which provides a large saving in computational efforts, is the well known one-point Gauss quadrature which is widely used for 4 nodes quadrilateral elements. On the other hand, the biggest disadvantage to one-point integration is the need to control the zero energy modes, called hourglassing modes, which arise. The efficiency of four different an...