TY - GEN
T1 - Estimating the geometric error of finite volume schemes for conservation laws on surfaces for generic numerical flux functions
AU - Giesselmann, Jan
AU - Müller, Thomas
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2014.
PY - 2014
Y1 - 2014
N2 - This contribution is concerned with finite volume schemes approximating scalar hyperbolic conservation laws on evolving hypersurfaces of ℝ3. Theoretical schemes assuming knowledge of all geometric quantities are compared to (practical) schemes defined on moving polyhedra approximating the surface. For the former schemes error estimates have already been proven, but the implementation of such schemes is not feasible for complex geometries. The latter schemes, in contrast, only require (easily) computable geometric quantities and are thus more useful for practical computations. In (Giesselmann and Müller Number. Math. 2014, doi:10.1007/s00211-014-0621-5) an estimate for the difference between solutions of both classes of schemes is proven. This estimate relies on an estimate for the geometric error of the numerical fluxes, which will be investigated in more detail in this contribution.
AB - This contribution is concerned with finite volume schemes approximating scalar hyperbolic conservation laws on evolving hypersurfaces of ℝ3. Theoretical schemes assuming knowledge of all geometric quantities are compared to (practical) schemes defined on moving polyhedra approximating the surface. For the former schemes error estimates have already been proven, but the implementation of such schemes is not feasible for complex geometries. The latter schemes, in contrast, only require (easily) computable geometric quantities and are thus more useful for practical computations. In (Giesselmann and Müller Number. Math. 2014, doi:10.1007/s00211-014-0621-5) an estimate for the difference between solutions of both classes of schemes is proven. This estimate relies on an estimate for the geometric error of the numerical fluxes, which will be investigated in more detail in this contribution.
UR - https://www.scopus.com/pages/publications/84927642489
U2 - 10.1007/978-3-319-05684-5_31
DO - 10.1007/978-3-319-05684-5_31
M3 - Conference contribution
AN - SCOPUS:84927642489
T3 - Springer Proceedings in Mathematics and Statistics
SP - 323
EP - 331
BT - Finite Volumes for Complex Applications VII - Methods and Theoretical Aspects, FVCA 7
A2 - Rohde, Christian
A2 - Fuhrmann, Jürgen
A2 - Ohlberger, Mario
PB - Springer New York LLC
T2 - 7th International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives, FVCA7
Y2 - 15 June 2014 through 20 June 2014
ER -