scholarly journals $L^1$-convergence rate of viscosity methods for scalar conservation laws with the interaction of elementary waves and the boundary

2004 ◽  
Vol 62 (4) ◽  
pp. 601-621 ◽  
Author(s):  
Hongxia Liu ◽  
Tao Pan
Keyword(s):  
Convergence Rate ◽  
Conservation Laws ◽  
Scalar Conservation Laws ◽  
Interaction Of Elementary Waves ◽  
Scalar Conservation ◽  
Elementary Waves

scholarly journals On a quadratic functional for scalar conservation laws

2014 ◽  
Vol 11 (02) ◽  
pp. 355-435 ◽  
Author(s):  
Stefano Bianchini ◽  
Stefano Modena
Keyword(s):  
Convergence Rate ◽  
Conservation Laws ◽  
Natural Extension ◽  
Approximate Solutions ◽  
Quadratic Functional ◽  
Scalar Conservation Laws ◽  
Nonlinear Case ◽  
Glimm Scheme ◽  
Quadratic Interaction ◽  
Scalar Conservation

We prove a quadratic interaction estimate for approximate solutions to scalar conservation laws obtained by the wavefront tracking approximation or the Glimm scheme. This quadratic estimate has been used in the literature to prove the convergence rate of the Glimm scheme. The proof is based on the introduction of a quadratic functional 𝔔(t), decreasing at every interaction, and such that its total variation in time is bounded. Differently from other interaction potentials present in the literature, the form of this functional is the natural extension of the original Glimm functional, and coincides with it in the genuinely nonlinear case.

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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