scholarly journals Optimal rate of convergence of a stochastic particle method to solutions of 1D viscous scalar conservation laws

2003 ◽  
Vol 73 (246) ◽  
pp. 777-813 ◽  
Author(s):  
Mireille Bossy
Keyword(s):  
Conservation Laws ◽  
Rate Of Convergence ◽  
Particle Method ◽  
Optimal Rate ◽  
Scalar Conservation Laws ◽  
Optimal Rate Of Convergence ◽  
Scalar Conservation ◽  
Stochastic Particle

DISCRETE COMPRESSIVE SOLUTIONS OF SCALAR CONSERVATION LAWS

2004 ◽  
Vol 01 (03) ◽  
pp. 493-520
Author(s):  
BRUNO DESPRÉS
Keyword(s):  
Theoretical Analysis ◽  
Conservation Laws ◽  
Rate Of Convergence ◽  
Numerical Experiments ◽  
Scalar Conservation Laws ◽  
Initial Profile ◽  
Fully Discrete ◽  
Discrete Approach ◽  
Scalar Conservation ◽  
Proof Of Convergence

We prove the convergence of numerical approximations of compressive solutions for scalar conservation laws with convex flux. This new proof of convergence is fully discrete and does not use Kuznetsov's approach. We recover the well-known rate of convergence in O(Δx½). With the same fully discrete approach, we also prove a rate of convergence in O(Δx) uniformly in time, if the initial data is a shock, or asymptotically after the compression of the initial profile. Numerical experiments confirm the theoretical analysis.

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
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