Journal
NUMERISCHE MATHEMATIK
Volume 144, Issue 4, Pages 751-785Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00211-020-01101-7
Keywords
Primary 35L65; Secondary 76L05; 76N
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-manifold with boundary referred to as a spacetime, and defined from a prescribed flux field of n-forms depending on a parameter (the unknown variable)-a class of equations proposed by LeFloch and Okutmustur (Far East J. Math. Sci. 31:49-83, 2008). Our main result is a proof of the convergence of the finite volume method for weak solutions satisfying suitable entropy inequalities. A main difference with previous work is that we allow for slices with a boundary and, in addition, introduce a new formulation of the finite volume method involving the notion of total flux functions. Under a natural global hyperbolicity condition on the flux field and the spacetime and by assuming that the spacetime admits a foliation by compact slices with boundary, we establish an existence and uniqueness theory for the initial and boundary value problem, and we prove a contraction property in a geometrically natural L1 type distance.
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