A Comparison of Constrained Finite Elements and Response Matrices as One-Dimensional Transport Approximations

A new coarse-mesh technique, the constrained finite element method, is formulated from the variational form of the even-parity transport equation: Linear finite elements in space are combined with a P₁ constraint on the angular trial functions at selected nodes to obtain a coarse-mesh three-point difference scheme for the scalar flux. Beginning with the same variational form of the transport equation, response matrix equations are derived that differ from the constrained finite element method only in the angular approximation made at the coarsemesh nodes. The two techniques are compared to each other, to S₈ reference solutions, and to diffusion calculations for a number of one-group slab geometry problems involving both homogeneous media and lattice cells; they are found to be of comparable accuracy and efficiency. The generalization of the constrained finite element method is discussed.