Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations

1. Numerical Homogenization Methods for Parabolic Monotone Problems
Assyr Abdulle

2. Virtual Element Implementation for General Elliptic Equations
Lourenco Beirão Veiga, Franco Brezzi, Luisa Donatella Marini, Alessandro Russo

3. On Quasi-Interpolation Operators in Spline Spaces
Annalisa Buffa, Eduardo M. Garau, Carlotta Giannelli, Giancarlo Sangalli

4. Stabilised Finite Element Methods for Ill-Posed Problems with Conditional Stability
Erik Burman

5. Static Condensation, Hybridization, and the Devising of the HDG Methods
Bernardo Cockburn

6. Robust DPG Methods for Transient Convection-Diffusion
Truman Ellis, Jesse Chan, Leszek Demkowicz

7. A Review of Hybrid High-Order Methods: Formulations, Computational Aspects, Comparison with Other Methods
Daniele A. Pietro, Alexandre Ern, Simon Lemaire

8. A Survey of Trefftz Methods for the Helmholtz Equation
Ralf Hiptmair, Andrea Moiola, Ilaria Perugia

9. Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains
Paola F. Antonietti, Andrea Cangiani, Joe Collis, Zhaonan Dong, Emmanuil H. Georgoulis, Stefano Giani, Paul Houston

10. Discretization of Mixed Formulations of Elliptic Problems on Polyhedral Meshes
Konstantin Lipnikov, Gianmarco Manzini

11. Variational Multiscale Stabilization and the Exponential Decay of Fine-Scale Correctors
Daniel Peterseim

12. Discontinuous Galerkin Methods for Time-Dependent Convection Dominated Problems: Basics, Recent Developments and Comparison with Other Methods
Chi-Wang Shu

13. Foundations of the MHM Method
Christopher Harder, Frédéric Valentin

14. Erratum to: A Survey of Trefftz Methods for the Helmholtz Equation
Ralf Hiptmair, Andrea Moiola, Ilaria Perugia

Keywords: Mathematics, Computational Science and Engineering, Partial Differential Equations