Comparison of finite-volume schemes for diffusion problems

Finite Volume Methods for Convection Diffusion Problems

Introduction In this paper we consider cell centered nite di erence approximations for second order convection di usion equations of divergence type Our goal is to construct nite di erence methods of second order of approximation that satisfy the discrete maximum principle The error estimates are in the discrete Sobolev spaces associated with the considered boundary value problem Approximation ...

Error estimates for higher-order finite volume schemes for convection-diffusion problems

It is still an open problem to prove a priori error estimates for finite volume schemes of higher order MUSCL type, including limiters, on unstructured meshes, which show some improvement compared to first order schemes. In this paper we use these higher order schemes for the discretization of convection dominated elliptic problems in a convex bounded domain Ω in IR2 and we can prove such kind ...

First-, second-, and third-order finite-volume schemes for diffusion

Monotone finite volume schemes for diffusion equations on polygonal meshes

Weconstruct a nonlinear finite volume (FV) scheme for diffusion equationon star-shapedpolygonalmeshes andprove that the scheme ismonotone, i.e., it preserves positivity of analytical solutions for strongly anisotropic and heterogeneous full tensor coefficients. Our scheme has only cell-centered unknowns, and it treats material discontinuities rigorously and offers an explicit expression for the...

Finite Volume Schemes for Nonlinear Parabolic Problems: Another Regularization Method

Abstract. On one hand, the existence of a solution to degenerate parabolic equations, without a nonlinear convection term, can be proven using the results of Alt and Luckhaus, Minty and Kolmogorov. On the other hand, the proof of uniqueness of an entropy weak solution to a nonlinear scalar hyperbolic equation, first provided by Krushkov, has been extended in two directions: Carrillo has handled...