The fast adaptive composite grid (FAC) method is an iterative method for solving discrete boundary value problems on composite grids. McCormick introduced the method in [10J and considered the convergence behaviour for discrete problems resulting from finite volume element discretiza-tion on composite grids. In this paper we consider discrete problems resulting from finite difference discretiza...

A p-multigrid (p=polynomial degree) discontinuous Galerkin method is presented for the solution of the compressible Euler equations on unstructured grids. The method operates on a sequence of solution approximations of different polynomial orders. A distinct feature of this p-multigrid method is the application of an explicit smoother on the higher level approximations (p > 0) and an implicit s...

We compare an iterative asynchronous parallel algorithm for the solution of partial diierential equations, with a synchronous algorithm , in terms of termination detection schemes and performance. Both algorithms are based on discontinuous Galerkin nite-element methods, in which the local elements provide a natural decomposition of the problem into computationally-independent sets. We demonstra...

In this paper we formulate and analyze a discretization method for a 2D linear singularly perturbed convection-diffusion problem with a singular perturbation parameter ε. The method is based on a nonconforming combination of the conventional Galerkin piecewise linear triangular finite element method and an exponentially fitted finite volume method, and on a mixture of triangular and rectangular...

We present here a number of test cases and meshes which were designed to form a benchmark for finite volume schemes and give a summary of some of the results which were presented by the participants to this benchmark. We address a two-dimensional anisotropic diffusion problem, which is discretized on general, possibly non-conforming meshes. In most cases, the diffusion tensor is taken to be ani...

A novel methodology for the simulation of 2D thermohaline double diffusive processes, driven by heterogeneous temperature and concentration fields in variable-density saturated porous media, is presented. The stream function is used to describe the flow field and it is defined in terms of mass flux. The partial differential equations governing system is given by the mass conservation equation o...

We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov–Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Fi...

We consider the initial boundary value problem for the homogeneous heat equation, with homogeneous Dirichlet boundary conditions. By the maximum principle the solution is nonnegative for positive time if the initial data are nonnegative. We study to what extent this property carries over to some piecewise linear finite element discretizations, namely the Standard Galerkin method, the Lumped Mas...

In recent years it has become clear that the current computational methods for scientific and engineering phenomena are inadequate for many challenging problems. Examples of these problems are wave propagation, turbulent fluid flow, as well as problems involving nonlinear interactions and multiple scales. This has resulted in a significant interest in so-called high-order accurate methods, whic...