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July 5, 2026Communications on Applied Mathematics and ComputationOpen Access

Variational Data Assimilation for the Wave Equation in Heterogeneous Media: Numerical Investigation of Stability

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Authors

EBErik BurmanJPJanosch PreußTBTim van Beeck

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Overview

Numerical investigation of wave equations reveals stability challenges in heterogeneous media.

Key Points

  • This investigation aims to determine if stability results in homogeneous media apply to a medium with jump discontinuities.
  • Numerical methods were developed for solving the wave equation under the unique continuation problem.
  • Lipschitz stability was analyzed based on geometric control conditions.
  • Comparisons were made between homogeneous and heterogeneous media using numerical experiments.
  • Results suggest that the stability properties do carry over to cases with jump discontinuities.
  • Computational demands significantly increase in heterogeneous media compared to homogeneous cases.

Cite This Study

Burman et al. (2026) studied this question.

synapsesocial.com/papers/6a49f36ff5d1d45b287ff7cahttps://doi.org/10.1007/s42967-026-00583-w
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