A Hodge Decomposition Finite Element Method for an Elliptic Maxwell Boundary Value Problem on General Polyhedral Domains

Key Points

• A Hodge decomposition approach effectively addresses elliptic Maxwell boundary value problems on general polyhedral domains, enhancing solution accuracy.
• Error analysis reveals necessary robustness for the presented method without relying on regularity assumptions, supporting its applicability across varied scenarios.
• Numerical results demonstrate the method's reliability in scalar elliptic problems and its performance with vector potentials in fluid flow studies.
• The study provides insights into the integration of Hodge decomposition with finite element methods for complex geometries, paving the way for future research.