TY - GEN
T1 - A multiscale sparse grid technique for a two-dimensional convection-diffusion problem with exponential layers
AU - Russell, Stephen
AU - Madden, Niall
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2015.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - We investigate the application of a multiscale sparse grid finite element method for computing numerical solutions to a two-dimensional singularly perturbed convection-diffusion problem posed on the unit square. Typically, sparse grid methods are constructed using a hierarchical basis (see, e.g., Bungartz and Griebel [1]). In our approach, the method is presented as a generalisation of the two-scale method described in Liu et al. [3], and is related to the combination technique outlined by Pflaum and Zhou [7]. We show that this method retains the same level of accuracy, in the energy norm, as both the standard Galerkin and two-scale methods. The computational cost associated with the method, however, is O(NlogN), compared to O(N2) and O(N3/2) for the Galerkin and two-scale methods respectively.
AB - We investigate the application of a multiscale sparse grid finite element method for computing numerical solutions to a two-dimensional singularly perturbed convection-diffusion problem posed on the unit square. Typically, sparse grid methods are constructed using a hierarchical basis (see, e.g., Bungartz and Griebel [1]). In our approach, the method is presented as a generalisation of the two-scale method described in Liu et al. [3], and is related to the combination technique outlined by Pflaum and Zhou [7]. We show that this method retains the same level of accuracy, in the energy norm, as both the standard Galerkin and two-scale methods. The computational cost associated with the method, however, is O(NlogN), compared to O(N2) and O(N3/2) for the Galerkin and two-scale methods respectively.
UR - https://www.scopus.com/pages/publications/84964851972
U2 - 10.1007/978-3-319-25727-3_19
DO - 10.1007/978-3-319-25727-3_19
M3 - Conference Publication
SN - 9783319257259
SN - 1439-7358
VL - 108
T3 - Lecture Notes in Computational Science and Engineering
SP - 245
EP - 255
BT - Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2014
A2 - Knobloch, Petr
PB - Springer-Verlag
T2 - Internatinal Conference on Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2014
Y2 - 15 September 2014 through 19 September 2014
ER -