Basic Numerical Methods for Scalar Conservation Laws

1998 ◽  
pp. 309-350
Keyword(s):  
Numerical Methods ◽  
Conservation Laws ◽  
Scalar Conservation Laws ◽  
Scalar Conservation

scholarly journals Continuous dependence and error estimation for viscosity methods

Acta Numerica ◽  
2003 ◽  
Vol 12 ◽  
pp. 127-180 ◽  
Author(s):  
Bernardo Cockburn
Keyword(s):  
Numerical Methods ◽  
Conservation Laws ◽  
Approximation Theory ◽  
Continuous Dependence ◽  
Entropy Solution ◽  
Viscosity Coefficient ◽  
Scalar Conservation Laws ◽  
Natural Approach ◽  
Scalar Conservation ◽  
Continuous Dependence Results

In this paper, we review some ideas on continuous dependence results for the entropy solution of hyperbolic scalar conservation laws. They lead to a complete L^\infty(L^1)-approximation theory with which error estimates for numerical methods for this type of equation can be obtained. The approach we consider consists in obtaining continuous dependence results for the solutions of parabolic conservation laws and deducing from them the corresponding results for the entropy solution. This is a natural approach, as the entropy solution is nothing but the limit of solutions of parabolic scalar conservation laws as the viscosity coefficient goes to zero.

scholarly journals Numerical Solution of Scalar Conservation Laws with Random Flux Functions

2016 ◽  
Vol 4 (1) ◽  
pp. 552-591 ◽  
Author(s):  
Siddhartha Mishra ◽  
Nils Henrik Risebro ◽  
Christoph Schwab ◽  
Svetlana Tokareva
Keyword(s):  
Conservation Laws ◽  
Numerical Solution ◽  
Scalar Conservation Laws ◽  
Scalar Conservation
Sign in / Sign up

Export Citation Format

Share Document