MAXIMUM PRINCIPLE AND CONVERGENCE OF CENTRAL SCHEMES BASED ON SLOPE LIMITERS Academic Article

abstract

• A maximum principle and convergence of second order central schemes is proven for scalar conservation laws in dimension one. It is well known that to establish a maximum principle a nonlinear piecewise linear reconstruction is needed and a typical choice is the minmod limiter. Unfortunately, this implies that the scheme uses a first order reconstruction at local extrema. The novelty here is that we allow local nonlinear reconstructions which do not reduce to first order at local extrema and still prove maximum principle and convergence. 2011 American Mathematical Society.

authors

• Popov, Bojan

published proceedings

• MATHEMATICS OF COMPUTATION

author list (cited authors)

• Mehmetoglu, O., & Popov, B.

citation count

• 4

complete list of authors

• Mehmetoglu, Orhan||Popov, Bojan

publication date

• January 2012

publisher

• American Mathematical Society (AMS)  Publisher

published in

• Mathematics of Computation  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics

Digital Object Identifier (DOI)

• 10.1090/S0025-5718-2011-02514-7

start page

• 219

end page

• 231

volume

• 81

issue

• 277