Abstract. We extend a well-balanced finite volume evolution Galerkin (FVEG) method to nonuniform grids. As a model problem, we consider the two-dimensional shallow water equations with a source term modelling the bottom topography. Our work is based on the well-balanced scheme proposed in (Lukáčová, Noelle, Kraft, J.Comp.Physics, 221, 2007). We present selected test cases to demonstrate the cap...

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...

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...

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 ...

We consider the efficient deterministic solution of elliptic boundary value problems with random diffusion matrix. Assuming random perturbations with known k moments, we derive, to leading order in the random perturbation’s amplitude, deterministic equations for k moments of the random solution. The solution’s k-th moment satisfies a k-fold tensor product boundary value problem on the k-fold pr...

In this article, element free Galerkin method is used for static analysis of thin micro/nanoscale plates based on the nonlocal plate theory. The problem is solved for the plates with arbitrary boundary conditions. Since shape functions of the element free Galerkin method do not satisfy the Kronecker’s delta property, the penalty method is used to impose the essential boundary conditions. Discre...