A Numerical Method for Handling Boundary and Transmission Conditions in Some Linear Partial Differential Equations

In this paper, we propose a method derived from a Nitsche approach for handling boundary and transmission conditions in some partial differential equations. Several years ago, the Nitsche method was introduced to impose weakly essential boundary conditions in the scalar Laplace operator. We propose here an extension to vector div −curl problems. Two examples of applications are presented. The first one is concerned with the Maxwell equations. This allows us to solve these equations, particularly in domains with reentrant corners, where the solution can be singular. The second example deals with the Navier-Lame equations. One can handle the case of a crack existence in a plate domain made of several different layers, characterized by different material properties. Numerical experiments are reported.