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Title of Journal: J Sci Comput

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Abbravation: Journal of Scientific Computing

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Springer US

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DOI

10.1007/bf01259432

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1573-7691

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Solving 1D Conservation Laws Using Pontryagin’s Mi

Authors: Wei Kang Lucas C Wilcox
Publish Date: 2016/10/04
Volume: 71, Issue: 1, Pages: 144-165
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Abstract

This paper discusses a connection between scalar convex conservation laws and Pontryagin’s minimum principle For flux functions for which an associated optimal control problem can be found a minimum value solution of the conservation law is proposed For scalar spaceindependent convex conservation laws such a control problem exists and the minimum value solution of the conservation law is equivalent to the entropy solution This can be seen as a generalization of the Lax–Oleinik formula to convex not necessarily uniformly convex flux functions Using Pontryagin’s minimum principle an algorithm for finding the minimum value solution pointwise of scalar convex conservation laws is given Numerical examples of approximating the solution of both spacedependent and spaceindependent conservation laws are provided to demonstrate the accuracy and applicability of the proposed algorithm Furthermore a MATLAB routine using Chebfun is provided along with demonstration code on how to use it to approximately solve scalar convex conservation laws with spaceindependent flux functions

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  1. A Hybridized Discontinuous Galerkin Method with Reduced Stabilization
  2. Exact Low-Rank Matrix Completion from Sparsely Corrupted Entries Via Adaptive Outlier Pursuit
  3. Efficient Rearrangement Algorithms for Shape Optimization on Elliptic Eigenvalue Problems
  4. Sparsity Enforcing Edge Detection Method for Blurred and Noisy Fourier data
  5. Semi-Lagrangian Runge-Kutta Exponential Integrators for Convection Dominated Problems
  6. The Finite Volume-Complete Flux Scheme for Advection-Diffusion-Reaction Equations
  7. Simulation of an $$n^{+}\hbox {-}n\hbox {-}n^{+}$$ Diode by Using Globally-Hyperbolically-Closed High-Order Moment Models
  8. Optimal Spectral-Galerkin Methods Using Generalized Jacobi Polynomials
  9. Theoretical and Numerical Investigation of the Finite Cell Method
  10. The Effect of the Consistent Mass Matrix on the Maximum-Principle for Scalar Conservation Equations
  11. Analysis of Nonlinear Spectral Eddy-Viscosity Models of Turbulence
  12. Transformation Methods for the Numerical Integration of Three-Dimensional Singular Functions
  13. A Posteriori Estimates for a Natural Neumann–Neumann Domain Decomposition Algorithm on a Unilateral Contact Problem
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