报告摘要：
| Interface problems arise in the fields of fluid dynamics, materials science, and computational biology. The numerical challenge comes from discontinuities of coefficients at the interface,where the solution is not smooth in general. Due to such irregularity, standard gradient recovery methods fail to give superconvergent results. In the talk, I will introduce my recent development of post-processing techniques for interface problems. In particular, I develop a series of gradient recovery methods based on the Cartesian mesh. Such type of numerical methods is able to resolve discontinuity without requiring mesh aligned with the interface. The superconvergence of proposed
post-processing strategies can be numerically verified and theoretically validated. I establish a theoretical framework of superconvergence analysis of finite element methods for interface problem on the Cartesian mesh. In addition, the proposed gradient recovery methods provide simple and asymptotically exact a posterior error estimators for interface problems. Applications to accelerate the computation of topological edge mode in photonic graphene with honeycomb structures will be also discussed.
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