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Mathematics > Numerical Analysis

arXiv:1804.08648 (math)
[Submitted on 23 Apr 2018]

Title:Structure preserving approximation of dissipative evolution problems

Authors:Herbert Egger
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Abstract:We present a general abstract framework for the systematic numerical approximation of dissipative evolution problems. The approach is based on rewriting the evolution problem in a particular form that complies with an underlying energy or entropy structure. Based on the variational characterization of smooth solutions, we are then able to show that the approximation by Galerkin methods in space and discontinuous Galerkin methods in time automatically leads to numerical schemes that inherit the dissipative behavior of the evolution problem. The proposed framework is rather general and can be applied to a wide range of applications. This is demonstrated by a detailed discussion of a variety examples ranging from diffusive partial differential equations to Hamiltonian and gradient systems.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:1804.08648 [math.NA]
  (or arXiv:1804.08648v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1804.08648

Submission history

From: Herbert Egger [view email]
[v1] Mon, 23 Apr 2018 18:18:36 UTC (18 KB)
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