The staggered discontinuous Galerkin (SDG) method is a finite element framework based on staggered primal–dual meshes, where scalar and flux variables are discretized on interlaced grids. This structure naturally ensures local conservation and stability while retaining the flexibility of discontinuous approximations.

In this talk, we present a new family of Raviart–Thomas staggered discontinuous Galerkin (RT-SDG) methods on general polygonal meshes. The method is formulated in a mixed setting, with the primal variable approximated in a locally H1-conforming space and the flux in a locally H(div)-conforming Raviart–Thomas space. The staggered mesh structure renders the classical RTk×Pk pair unstable; this is overcome by enriching the primal space with bubble functions on dual elements, leading to inf–sup stability and optimal convergence. Some applications to interface problems are also discussed

 The RT-SDG framework extends naturally to arbitrary-order discretizations of second-order elliptic eigenvalue problems on polygonal meshes. The resulting schemes are spurious-free, preserve local and global conservation laws, reduce to symmetric positive definite systems involving only the primal variable without hybridization, and require no extrinsic stabilization. Using Fortin-type operators with modified commuting properties, we establish optimal convergence of both eigenvalues and eigenfunctions, together with L2-superconvergence of eigenfunctions. Numerical experiments confirm the theory and demonstrate the robustness of the methods.

Short Bio: Eun-Jae Park is Professor of Computational Science and Engineering at Yonsei University, Seoul. He received his Ph.D. from Purdue University in 1993 and held academic positions in the United States and Europe before joining Yonsei. His research focuses on the numerical analysis of partial differential equations, with particular emphasis on structure-preserving finite element methods on general meshes, including staggered discontinuous Galerkin methods, hybrid and mixed formulations, and virtual element methods. He has published extensively in international journals and has delivered plenary and invited talks at several international conferences in numerical analysis. He has also organized a number of international conferences, including ICOSAHOM 2023.