 
Summary: A geometric approach to error estimates for
conservation laws posed on a spacetime
Paulo Amorim1
, Philippe G. LeFloch2
, and Wladimir Neves3
February 16, 2010
Abstract
Weconsiderahyperbolicconservationlawposedonan(N+1)dimensio
nal spacetime, whose flux is a field of differential forms of degree N. Gen
eralizing the classical Kuznetsov's method, we derive an L1
error estimate
which applies to a large class of approximate solutions. In particular, we
apply our main theorem and deal with two entropy solutions associated
with distinct flux fields, as well as with an entropy solution and an approxi
mate solution. Our framework encompasses, for instance, equations posed
on a globally hyperbolic Lorentzian manifold.
1 Introduction
This paper provides a general framework leading to error estimates for hyper
bolic conservation laws posed on an (N + 1)dimensional manifold M, referred
to as a spacetime and, in particular, leading to a sharp estimate for the differ
