Error analysis of staggered finite difference finite volume schemes on unstructured meshes

Staggered Finite Difference Schemes for Conservation Laws

In this work, we introduce new finite-difference shock-capturing central schemes on staggered grids. Staggered schemes may have better resolution of the corresponding unstaggered schemes of the same order. They are based on high order non oscillatory reconstruction (ENO or WENO), and a suitable ODE solver for the computation of the integral of the flux. Although they suffer from a more severe s...

Staggered Finite Difference Schemes for Balance Laws

In this paper a new family of high-order finite-difference shock-capturing central schemes for hyperbolic systems with stiff source is presented. The schemes are based on recently developed finite difference discretization on staggered grids, coupled with implicit-explicit (IMEX) time discretization for an efficient treatment of the source term. Numerical tests show the robustness and accuracy ...

Nonstandard finite difference schemes for differential equations

In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...

Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes

We consider a nonlinear finite volume (FV) scheme for stationary diffusion equation. We prove that the scheme is monotone, i.e. it preserves positivity of analytical solutions on arbitrary triangular meshes for strongly anisotropic and heterogeneous full tensor coefficients. The scheme is extended to regular star-shaped polygonal meshes and isotropic heterogeneous coefficients.

Entropy Conservative and Entropy Stable Finite Volume Schemes for Multi-dimensional Conservation Laws on Unstructured Meshes