A novel strategy for the Hybridizable Discontinuous Galerkin (HDG) solution of heat bimaterial problems is proposed. It is based on eXtended Finite Element philosophy, together with a level set description of interfaces. Heaviside enrichment on cut elements and cut faces is used to represent discontinuities across the interface. A suitable weak form for the HDG local problem on cut elements is ...

The local projection method is applied to inf-sup stable discretisations of the Oseen problem. Error bounds of order r are proven for known inf-sup stable pairs of finite element spaces which approximate velocity and pressure by elements of order r and r− 1, respectively. In case of a positive reaction coefficient, the error constants are robust with respect to the viscosity but depend on the p...

This paper presents a new adaptive multiscale homogenization scheme for the simulation of damage and fracture in concrete structures. A two-scale homogenization method, coupling meso-scale discrete particle models to macroscale finite element models, is formulated into an adaptive framework. A continuum multiaxial failure criterion for concrete is calibrated on the basis of fine-scale simulatio...

Abstract. We propose a mixed discontinuous Galerkin method for the bending problem of Naghdi shell, and present an analysis for its accuracy. The error estimate shows that when components of the curvature tensor and Christoffel symbols are piecewise linear functions, the finite element method has the optimal order of accuracy, which is uniform with respect to the shell thickness. Generally, the...

An adapted deflation preconditioner is employed to accelerate the solution of linear systems resulting from discretization fracture mechanics problems with well-conditioned extended/generalized finite elements. The space typically used for elasticity enriched additional vectors, accounting enrichment functions used, thus effectively removing low frequency components error. To further improve pe...

This paper presents an optimum technique based on the least squares method for the derivation of the bubble functions to enrich the standard linear finite elements employed in the formulation of Galerkin weighted-residual statements. The element-level linear shape functions are enhanced with supplementary polynomial bubble functions with undetermined coefficients. The best least squares minimiz...

In this paper, a modification on the fixed grid finite element method is presented and used in the solution of 2D linear elastic problems. This method uses non-boundary-fitted meshes for the numerical solution of partial differential equations. Special techniques are required to apply boundary conditions on the intersection of domain boundaries and non-boundary-fitted elements. Hence, a new met...

The symmetric coupling of mixed nite element and boundary element methods is analysed for a model interface problem with the Laplacian. The coupling involves a further continuous ansatz function on the interface to link the discontinuous displacement eld to the necessarily continuous boundary ansatz function. Quasi-optimal a priori error estimates and sharp a posteriori error estimates are esta...