A Mixed Method for Axisymmetric Div-Curl Systems

We present a mixed method for a three-dimensional axisymmetric div-curl system reduced to a two-dimensional computational domain via cylindrical coordinates. We show that when the meridian axisymmetric Maxwell problem is approximated by a mixed method using the lowest order Nédélec elements (for the vector variable) and linear elements (for the Lagrange multiplier), one obtains optimal error estimates in certain weighted Sobolev norms. The main ingredient of the analysis is a sequence of projectors in the weighted norms satisfying some commutativity properties

The Paleozoic Origin of Enzymatic Lignin Decomposition Reconstructed from 31 Fungal Genomes

Wood is a major pool of organic carbon that is highly resistant to decay, owing largely to the presence of lignin. The only organisms capable of substantial lignin decay are white rot fungi in the Agaricomycetes, which also contains non–lignin-degrading brown rot and ectomycorrhizal species. Comparative analyses of 31 fungal genomes (12 generated for this study) suggest that lignin-degrading peroxidases expanded in the lineage leading to the ancestor of the Agaricomycetes, which is reconstructed as a white rot species, and then contracted in parallel lineages leading to brown rot and mycorrhizal species. Molecular clock analyses suggest that the origin of lignin degradation might have coincided with the sharp decrease in the rate of organic carbon burial around the end of the Carboniferous period

MULTIGRID IN A WEIGHTED SPACE ARISING FROM AXISYMMETRIC ELECTROMAGNETICS

Abstract. Consider the space of two-dimensional vector functions whose components and curl are square integrable with respect to the degenerate weight given by the radial variable. This space arises naturally when modeling electromagnetic problems under axial symmetry and performing a dimension reduction via cylindrical coordinates. We prove that the multigrid V-cycle applied to the inner product in this space converges, provided certain modern smoothers are used. For the convergence analysis, we first prove several intermediate results, e.g., the approximation properties of a commuting projector in weighted norms, and a superconvergence estimate for a dual mixed method in weighted spaces. The uniformity of the multigrid convergence rate with respect to meshsize is then established theoretically and illustrated through numerical experiments. 1