The interface problems which involve partial differential equations having discontinuous coefficients across certain interfaces are often encountered in fluid dynamics, electromagnetics and materials science. Because of the low global regularity and the irregular geometry of the interface, the standard numerical methods which are efficient for smooth solutions usually lead to loss in accuracy across the interface. For arbitrarily shaped interface Γ, it is known that optimal or nearly optimal convergence rate can be recovered if body-fitted finite element meshes are used, see e.g. [6, 8, 20, 29]. Here, by "body-fitted meshes" we mean an element of the underlying mesh is required to intersect with the interface only through its boundaries (Fig. 1).
展开▼
