Why nonconservative schemes converge to wrong solutions: error analysis

Why Nonconservative Schemes Converge to Wrong Solutions: Error Analysis

This paper attempts to give a qualitative and quantitative description of the numerical error introduced by using finite différence schemes in nonconservative form for scalar conservation laws. We show that these schemes converge strongly in L^ norm to the solution of an inhomogeneous conservation law containing a Borel measure source term. Moreover, we analyze the properties of this Borel meas...

Why is cheating wrong?

It seems so obvious that cheating is wrong that providing a justification is not a main concern: most of the research is empirical and focuses on quantification and correlations. I look at a number of reasons why cheating may be wrong: it provides an unfair advantage over other students, it hinders learning, and it is dishonest. They are unexpectedly weak (often not proving that cheating is wro...

Wrong Way Recollement for Schemes

Here X is a topological space equal to the union of the closed subset Z and the open complement U , and D(Z), D(X), and D(U) are suitable derived categories of sheaves. The triangulated functors in a recollement must satisfy various conditions, most importantly that (i, i∗), (i∗, i ), (j!, j ), and (j, j∗) are adjoint pairs. The purpose of this note is to point out that, somewhat surprisingly, ...

Why is research fraud wrong?

Entropy Conservative and Entropy Stable Schemes for Nonconservative Hyperbolic Systems

The vanishing viscosity limit of nonconservative hyperbolic systems depends heavily on the specific form of the viscosity. Numerical approximations, such as the path consistent schemes of [C. Parés, SIAM J. Numer. Anal., 41 (2007), pp. 169–185], may not converge to the physically relevant solutions of the system. We construct entropy stable path consistent (ESPC) schemes to approximate nonconse...