Mortar Element Method for Flow Problems in Primitive Variables Form

Parallel implementation of the finite element method for the Helmholtz equation and the Stokes equations is discussed in the environment of a distributed-memory massively parallel computer where data is shared among the processors by communication procedures called message-passing. For implementation of the finite element methods based on domain decomposition, “pre-assembly type” and “restriction type” are introduced for data on nodal points. They simplify the implementation and reduce the amount of message-passing between subdomains. In order to reduce this further, the mortar element method is applied to the primitive variables of the Stokes equations. It maintains natural treatment of stress boundary conditions, which is an advantage of the finite element method. Its implementation can be described concisely by the idea of the two data types.