By discretizing an argument of Kislyakov, Naor and Schechtman proved that the 1-Wasserstein metric over the planar grid
This content will become publicly available on November 1, 2024
In this paper, we consider the linear convection-diffusion equation in one dimension with periodic boundary conditions, and analyze the stability of fully discrete methods that are defined with local discontinuous Galerkin (LDG) methods in space and several implicit-explicit (IMEX) Runge-Kutta methods in time. By using the forward temporal differences and backward temporal differences, respectively, we establish two general frameworks of the energy-method based stability analysis. From here, the fully discrete schemes being considered are shown to have monotonicity stability, i.e. the
- Award ID(s):
- 2010107
- NSF-PAR ID:
- 10498236
- Publisher / Repository:
- AMS
- Date Published:
- Journal Name:
- Mathematics of Computation
- Volume:
- 92
- Issue:
- 344
- ISSN:
- 0025-5718
- Page Range / eLocation ID:
- 2475 to 2513
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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has -distortion bounded below by a constant multiple of . We provide a new “dimensionality” interpretation of Kislyakov’s argument, showing that if is a sequence of graphs whose isoperimetric dimension and Lipschitz-spectral dimension equal a common number , then the 1-Wasserstein metric over has -distortion bounded below by a constant multiple of . We proceed to compute these dimensions for -powers of certain graphs. In particular, we get that the sequence of diamond graphs has isoperimetric dimension and Lipschitz-spectral dimension equal to 2, obtaining as a corollary that the 1-Wasserstein metric over has -distortion bounded below by a constant multiple of . This answers a question of Dilworth, Kutzarova, and Ostrovskii and exhibits only the third sequence of -embeddable graphs whose sequence of 1-Wasserstein metrics is not -embeddable. -
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