An error bound for the polygonal approximation of conservation laws with source terms

Error Bounds of Nite Diierence Schemes for Multi-dimensional Scalar Conservation Laws with Source Terms

This paper studies explicit and semi-implicit nite diierence schemes approximating non-homogeneous multi-dimensional scalar conservation laws with both stii and non-stii source terms. Error bounds of order O(p t) are presented for both cases.

Finite Difference Schemes for Scalar Conservation Laws with Source Terms

Explicit and semi{implicit nite diierence schemes approximating nonhomogenous scalar conservation laws are analyzed. Optimal error bounds independent of the stiiness of the underlying equation are presented.

Zero Reaction Limit for Hyperbolic Conservation Laws with Source Terms

In this paper we study the zero reaction limit of the hyperbolic conservation law with stii source term @ t u + @ x f(u) = 1 u(1 ? u 2) : For the Cauchy problem to the above equation, we prove that as ! 0, its solution converges to piecewise constant (1) solution, where the two constants are the two stable local equilibrium. The constants are separated by either shocks that travel with speed 1 ...

An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions

We study the parabolic approximation of a multidimensional scalar conservation law with initial and boundary conditions. We prove that the rate of convergence of the viscous approximation to the weak entropy solution is of order η, where η is the size of the artificial viscosity. We use a kinetic formulation and kinetic techniques for initial-boundary value problems developed by the last two au...

Error Estimate for Godunov Approximation of Locally Constrained Conservation Laws