Manuscript Topics

Partial differential equations play a fundamental role in modeling complex phenomena in physics, engineering, and biology. Structure-preserving numerical methods are designed to retain intrinsic geometric, topological, or physical properties of the continuous system—such as symplecticity, energy conservation, or divergence-free constraints—when discretized. These methods not only enhance numerical stability and long-term accuracy but also ensure that the computed solutions respect the underlying mathematical structure of the original problem. This special issue focuses on recent advances in structure-preserving techniques, including (but not limited to) geometric integrators, mimetic discretizations, conservative finite element/difference/volume schemes, and machine learning-aided approaches for PDEs. Contributions addressing theoretical analysis, algorithmic development, and applications in science and engineering are particularly welcome.

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