A stable and accurate hybrid FE-FD method

Sammanfattning: We develop a hybrid method to couple finite difference methods and finite element methods in a nonconforming multiblock fashion. The aim is to optimize computational efficiency when complex geometries present. The proposed coupling technique requires minimal changes in the existing schemes while maintaining strict stability, accuracy, and conservation. Analysis and computational results are shown for a linear problem (to the advection-diffusion equation) and a nonlinear problem (to the viscous Burger's equation) in two spatial dimensions