A linear algebraic approach to representing and computing finite elements
نویسنده
چکیده
We use standard ideas from numerical linear algebra plus orthogonal bases for polynomials to compute abstract finite elements. We express nodal bases in terms of orthogonal ones. This paradigm allows us to differentiate polynomials, evaluate local bilinear forms, and compute with affine equivalent elements. It applies not only to Lagrangian elements, but also to Hermite elements, H(div) and H(curl) elements, and elements subject to constraints. MSC: 65F30 (other matrix algorithms), 65N30 (finite elements)
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