In this work we design hybrid continuous-discontinuous finite element spaces that permit discontinuities on non-matching element interfaces of non-conforming meshes. Then, we develop an equal-order stabilized finite element formulation for incompressible flows over these hybrid spaces, which combines the element interior stabilization of SUPGtype continuous Galerkin formulations and the jump st...

We present a higher order accurate discontinuous Galerkin finite element method for the simulation of linear free-surface gravity waves. The method uses the classical Runge-Kutta method for the time discretization of the free-surface equations and the discontinuous Galerkin method for the space discretization. In order to circumvent numerical instabilities arising from an asymmetric mesh a stab...

The paper is concerned with the discontinuous Galerkin finite element method for the numerical solution of nonlinear conservation laws and nonlinear convection-diffusion problems with emphasis on applications to the simulation of compressible flows. We discuss two versions of this method: (a) Finite volume discontinuous Galerkin method, which is a generalization of the combined finite volume—fi...

We present a space-time finite element formulation of the Navier-Stokes equations which is stabilized via the Galerkin/least-squares approach. The variational equation is based on the time discontinuous Galerkin method and is written in terms of the physical entropy variables over the moving and deforming space-time slabs. The formulation thus becomes analogous to the classical arbitrary Lagran...

An incremental symmetric boundary integral formulation for the problem of many domains connected by non-linear cohesive interfaces is here presented. The problem of domains with traction-free cracks and/or rigid connections are particular instances of the proposed cohesive formulation. The numerical approximation of the considered problem is achieved by the symmetric Galerkin boundary element m...

We present different innovative formulations for shear deformable beams and plates exploiting the high inter-element continuity provided by NURBS basis functions. We develop isogeometric collocation methods in standard and mixed formulations as well as Galerkin methods using an alternative set of discrete variables. All methods are free of shear locking, which is confirmed by numerical tests.