Verification of high-order mixed FEM solution of transient Magnetic diffusion problems

摘要: We develop and present high order mixed finite element discretizations of the time dependent electromagnetic diffusion equations for solving eddy current problems on 3D unstructured grids. The are based H(grad), H(curl) H(div) conforming spaces combined with an implicit unconditionally stable generalized Crank-Nicholson differencing method. three separate formulations, namely E (electric field), H (magnetic field) A-{phi} (potential) formulations. For each formulation, we also provide a consistent procedure computing secondary variables F (current flux density) B density), as these fields required computation force heating terms. verify error convergence properties formulation via series numerical experiments canonical known analytic solutions. key result is that different formulations equally accurate, even J B, hence choice which to use depends mostly upon relevance Natural Essential boundary conditions problem interest. In addition, highlight issues verification methods can lead false conclusions accuracy methods.