$\mathbf{H}(\text{curl})$-reconstruction of piecewise polynomial fields with application to $hp$-a posteriori nonconforming error analysis for Maxwell's equations

Zhaonan Dong, Alexandre Ern

We devise and analyse a novel $\mathbf{H}(\text{curl})$-reconstruction operator for piecewise polynomial fields on shape-regular simplicial meshes. The (non-polynomial) recon…