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An \(hp\)-adaptive finite element method for electromagnetics. I: Data structure and constrained approximation. (English) Zbl 0979.78031
Summary: This is the first of several papers describing an implementation of the \(hp\)-adaptive, mixed finite element (FE) method for the solution of steady-state Maxwell’s equations proposed in L. Demkowicz and L. Vardapetyan [Comput. Methods Appl. Mech. Eng. 152, 103-124 (1998; Zbl 0994.78011)]. The discretization is defined on a hybrid grid consisting of both triangles and quads and allows for both \(h\)- and \(p\)-refinements of the mesh. The paper focuses on the data structure and constrained approximation issues and provides a number of illustrative examples.

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
78A25 Electromagnetic theory (general)
35Q60 PDEs in connection with optics and electromagnetic theory
2Dhp90; HP90
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