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Hilbert Complexes with Mixed Boundary Conditions -- Part 3: Biharmonic Complexes
Dirk Pauly, Michael Schomburg
We show that the biharmonic Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings whi…
Hilbert Complexes with Mixed Boundary Conditions -- Part 2: Elasticity Complex
Dirk Pauly, Michael Schomburg
We show that the elasticity Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings whi…
Hilbert Complexes with Mixed Boundary Conditions -- Part 1: De Rham Complex
Dirk Pauly, Michael Schomburg
We show that the de Rham Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings which…
The Elasticity Complex: Compact Embeddings and Regular Decompositions
Dirk Pauly, Walter Zulehner
We investigate the Hilbert complex of elasticity involving spaces of symmetric tensor fields. For the involved tensor fields and operators we show closed ranges, Friedrichs/Poincar…
Low Frequency Asymptotics and Electro-Magneto-Statics for Time-Harmonic Maxwell's Equations in Exterior Weak Lipschitz Domains with Mixed Boundary Conditions
Frank Osterbrink, Dirk Pauly
We prove that the time-harmonic solutions to Maxwell's equations in a 3D exterior domain converge to a certain static solution as the frequency tends to zero. We work in weighted S…
Poincare-Friedrichs Type Constants for Operators Involving grad, curl, and div: Theory and Numerical Experiments
Dirk Pauly, Jan Valdman
We give some theoretical as well as computational results on Laplace and Maxwell constants. Besides the classical de Rham complex we investigate the complex of elasticity and the c…