Mixed methods and the marriage between “mixed” finite elements and boundary elements

When fields that describe a physical situation extend over the whole space, but with complex behavior (nonlinearity, coupling, etc.) only in a bounded region and simple behavior in the rest of space, it may be worthwhile to treat the inner field by a finite elements procedure and the outer field by boundary elements. We address this “marriage” problem in the case of mixed elements. The model problem adopted for this discussion is magnetostatics. A new approach to the question of mixed elements is used, which emphasizes their parenthood with a classical concept of differential geometry, Whitney forms.

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