Numerical Analysis
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CEM-GMsFEM: Efficient Solution for High-Contrast Heterogeneous PDEs
This review details the Constrained Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for solving elliptic PDEs with high contrast heterogeneous coefficients. The method constructs multiscale basis functions using spectral auxiliary spaces and an oversampling strategy, whic…
Exact Noether Charge Conservation Drives Automatic Mesh Refinement in Discrete IBVPs
A variational action formulation treats coordinate maps as dynamical degrees of freedom alongside propagating fields in IBVPs, preserving space-time symmetries post-discretization for exact Noether charge conservation. This dynamical adjustment of coordinates enables automatic adaptive mesh refineme…