We consider the hp–version interior penalty discontinuous Galerkin finite element method (hp–DGFEM) for semilinear parabolic equations with mixed Dirichlet and Neumann boundary conditions. Our main concern is the error analysis of the hp–DGFEM on shape–regular spatial meshes. We derive error bounds under various hypotheses on the regularity of the solution, for both the symmetric and non–symmet...

In turbulence applications, strongly imposed no-slip conditions often lead to inaccurate mean flow quantities for coarse boundary-layer meshes. To circumvent this shortcoming, weakly imposed Dirichlet boundary conditions for fluid dynamics were recently introduced in [4]. In the present work, we propose a modification of the original weak boundary condition formulation that consistently incorpo...

The concept of fairing applied to triangular meshes with irregular connectivity has become more and more important. Previous contributions proposed a variety of fairing operators for manifolds and applied them to design multiresolution representations and editing tools for meshes. In this paper, we generalize these powerful techniques to handle non-manifold models. We propose a method to constr...

We present new finite element methods for Helmholtz and Maxwell equations for general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coeffic...

General Curvilinear Ocean Model (GCOM) is a coastal ocean model curvilinear in 3 dimensions, developed by Carlos Torres et al. The model uses a direct numerical simulation (DNS) approach to solve the primitive Navier-Stokes equations and uses boundary fitted Curvilinear coordinates; therefore, it is possible to use GCOM in various topographies and meshes. GCOM is currently being coupled with he...

The application of fictitious domain methods to the three-dimensional Helmholtz equation with absorbing boundary conditions is considered. The finite element discretization is performed by using locally fitted meshes, and algebraic fictitious domain methods with separable preconditioners are used in the iterative solution of the resultant linear systems. These methods are based on embedding the...

A new higher-order accurate method is proposed that combines the advantages of the classical p-version of the FEM on body-fitted meshes with embedded domain methods. A background mesh composed by higher-order Lagrange elements is used. Boundaries and interfaces are described implicitly by the level set method and are within elements. In the elements cut by the boundaries or interfaces, an autom...

In this paper we consider mesh approximations of a boundary value problem for singularly perturbed elliptic equations of convection-diffusion type on a strip. To approximate the equations, we use classical finite difference approximations on piecewise-uniform meshes condensing in a neighbourhood of the boundary layer. The approximation errors of solutions and derivatives are analysed in the ρ-m...

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and eve...