A More Accurate Green Element Method In Two And Three Spatial Dimensions
Author(s)
R. Pecher, S.D. Harris, R.J. Knipe, L. Elliott & D.B. Ingham
Abstract
A more accurate Green element method in two
and three spatial dimensions
Abstract
The Green element method is a powerful technique for solving nonlinear
boundary value problems. Derived from the boundary element method, over the
meshes of the finite element method, the GEM combines the second-order
accuracy of the BEM with the efficiency and versatility of the FEM.
The high accuracy of the Green element method, resulting from the direct
representation of normal fluxes as unknowns, comes at the price of very large
matrices for problems in 2D and 3D domains. The reason for this is a larger
number of inter-element boundaries connected to each internal node, yielding the
same number of the normal fluxes to be determined. The currently available
technique to avoid this problem approximates the normal fluxes by
differentiating the potential estimates within each element. Although this
approach produces much smaller matrices, the overall accuracy of the GEM is
sacrificed.
Keywords
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