This paper discusses the key-properties from the Parallel Finite Element Method (PFEM). It focuses at the PFEM applications in the context of non-conforming finite element basis functions (for maximal parallelism) on locally-bisection-refined tensor-product grids (for simple and cheap load balance techniques).

The Parallel Finite Element Method is an iterative solution method based on a Red-Black domain decomposition. The method is robust, and can solve elliptic as well as mixed elliptic-hyperbolic and hyperbolic problems. The amount of iterations is optimal for a method with only local communication. Nonlinear as well as constraint systems of equations can be solved element-wise in parallel.

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