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Finite elements of dimensions zero, one, two, and three are used to model electromagnetic coupling and shielding. Elements of dimension zero represent circuit elements, while those of dimension one can represent wires. In addition to ordinary two- and three-dimensional (2- and 3-D) finite elements, asymptotic finite elements are discussed for modeling fields extending to infinity. The models with finite elements of mixed dimension are used to compute capacitance and inductance matrices and their related coupled voltages and currents. A mixed-dimensional finite-element model of an electromagnetic shielding enclosure is constructed, and its computed dynamic leakage fields are shown to agree with measurement.