A new H(div)-conforming p-interpolation operator in two dimensions

2009/10/20 by Alex Bespalov, Bespalov, Alexei, Norbert Heuer +1
Engineering · #41A10 #65N15 #65N38 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.0910.3891

openalex publication_date 2009/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we construct a new H(div)-conforming projection-based p-interpolation operator that assumes only H^r(K) ∩ H^-1/2(div,K)-regularity (r > 0) on the reference element K (either triangle or square). We show that this operator is stable with respect to polynomial degrees and satisfies the commuting diagram property. We also establish an estimate for the interpolation error in the norm of the space H^-1/2(div,K), which is closely related to the energy spaces for boundary integral formulations of time-harmonic problems of electromagnetics in three dimensions.

Citations

• Discrete compactness for the p-version of discrete differential forms
• Convergence of the Natural hp-BEM for the Electric Field Integral Equation on Polyhedral Surfaces
• The hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces: a priori error analysis

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