Recently, Courbet and Croisille [Math. Model. Numer. Anal., 32, 631–649, 1998] introduced the FV box-scheme for the 2D Poisson problem in the case of triangular meshes. Generalization to higher degree box-schemes has been published by Croisille and Greff [Numer. Methods Partial Differential Equations, 18, 355–373, 2002]. These box-schemes are based on the idea of the finite volume method in tha...

Abstract We prove existence results for a reaction-diffusion system modeling the spread of early tumors. The existence result is proved by the Faedo-Galerkin method, a priori estimates and the compactness method. Moreover, we construct a finite volume scheme to our model, we establish existence of discrete solutions to this scheme, and show that it converges to a weak solution. Finally, some nu...

We present two new large time step methods within the framework of the wellbalanced finite volume evolution Galerkin (FVEG) schemes. The methodology will be illustrated for low Froude number shallow water flows with source terms modeling the bottom topography and Coriolis forces, but results can be generalized to more complex systems of balance laws. The FVEG methods couple a finite volume form...

This paper deals with intrusive Galerkin projection methods with Roe-type solver for uncertain hyperbolic systems using a finite volume discretization in physical space and a piecewise continuous representation at the stochastic level. The aim of this paper is to design a cost-effective adaptation of the deterministic Dubois and Mehlman corrector to avoid entropy-violating shocks in the presenc...

In this article, a one parameter family of discontinuous Galerkin finite volume element methods for approximating the solution of a class of second-order linear elliptic problems is discussed. Optimal error estimates in L2 and broken H 1norms are derived. Numerical results confirm the theoretical order of convergences. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 25: 140...

The modern vision of a flow solver necessarily includes adaptivity. In particular, mesh adaptivity enables the solution strategy to allocate the resources efficiently, in that cells are concentrated in areas where they are needed, as opposed to uniform mesh refinement. Multiresolution-based mesh adaptivity using biorthogonal wavelets has been quite successful with finite volume solvers for comp...

This work proposes a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations. The proposed reduced-order models associate with optimization problems characterized by a minimum-residual objective function and nonlinear equality constraints that explicitly enfo...

In this paper, we present a collection of algorithmic tools for constraining high-order discontinuous Galerkin (DG) approximations to hyperbolic conservation laws. We begin with a review of hierarchical slope limiting techniques for explicit DG methods. A new interpretation of these techniques leads to an unconditionally stable implicit algorithm for steady-state computations. The implicit glob...

A nonlinear formulation of the Meshless Local Petrov-Galerkin (MLPG) finite-volume mixed method is developed for the large deformation analysis of static and dynamic problems. In the present MLPG large deformation formulation, the velocity gradients are interpolated independently, to avoid the time consuming differentiations of the shape functions at all integration points. The nodal values of ...

This paper investigates the application of the Red-Black Half-Sweep Gauss-Seidel (HSGS-RB) method by using the half-sweep triangle finite element approximation equation based on the Galerkin scheme to solve two-dimensional Poisson equations. Formulations of the full-sweep and half-sweep triangle finite element approaches in using this scheme are also derived. Some numerical experiments are cond...