High-order discontinuous Galerkin method for curved boundary domains

The ever-increasing complexity of real-world applications has raised important challenges in the search for accurate and efficient numerical methods for solving partial differential equations. In particular, we are interested in modelling light propagation in the human cornea, where curvature and microstructural organisation have a strong influence on physical behaviour and pose significant challenges for the accurate numerical simulation of these phenomena. To address these challenges, we present a high-order numerical approach based on discontinuous Galerkin methods combined with a polynomial reconstruction strategy. This approach effectively handles curved boundary domains without relying on curved meshes and preserves the optimal convergence order that is often lost with standard polygonal approximations. The proposed method is supported by theoretical analysis and validated through numerical tests.

Contatti:
paola.antonietti@polimi.it
luca.formaggia@polimi.it