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Title: Tent-pitcher spacetime discontinuous Galerkin method for one-dimensional linear hyperbolic and parabolic PDEs
We present a spacetime DG method for 1D spatial domains and three linear hyperbolic, damped hyperbolic, and parabolic PDEs. The latter two correspond to Maxwell-Cattaneo-Vernotte (MCV) and Fourier heat conduction problems. The method is called the tent-pitcher spacetime DG method (tpSDG) due to its resemblance to the causal spacetime DG method (cSDG) wherein the solution advances in time by pitching spacetime patches. The tpSDG method extends the applicability of such methods from hyperbolic to parabolic and hyperbolic PDEs. For problems with a spatially uniform mesh, a transfer matrix approach is derived wherein the inflow, boundary, and source term values are mapped to the solution coefficient and output values. This resembles a finite difference scheme, but with grid points at the Gauss points of the spatial elements and arbitrarily tunable order of accuracy in spacetime. The spectral stability analysis of the method provides stability correction factors for the parabolic case. Numerical examples demonstrate the applicability of the method to problems with heterogeneous material properties.  more » « less
Award ID(s):
2039472
PAR ID:
10481528
Author(s) / Creator(s):
;
Publisher / Repository:
Elsevier
Date Published:
Journal Name:
Computers & Mathematics with Applications
Volume:
148
Issue:
C
ISSN:
0898-1221
Page Range / eLocation ID:
26 to 40
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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