All Outputs (4)

Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains (2016)
Book Chapter
Antonietti, P., Cangiani, A., Collis, J., Dong, Z., Georgoulis, E., Giani, S., & Houston, P. (2016). Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains. In G. Barrenechea, F. Brezzi, A. Cangiani, & E. Georgoulis (Eds.), Building bridges : connections and challenges in modern approaches to numerical partial differential equations (279-308). Springer Verlag. https://doi.org/10.1007/978-3-319-41640-3_9

The numerical approximation of partial differential equations (PDEs) posed on complicated geometries, which include a large number of small geometrical features or microstructures, represents a challenging computational problem. Indeed, the use of st... Read More about Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains.

Efficient and reliable hp-FEM estimates for quadratic eigenvalue problems and photonic crystal applications (2016)
Journal Article
Engström, C., Giani, S., & Grubišić, L. (2016). Efficient and reliable hp-FEM estimates for quadratic eigenvalue problems and photonic crystal applications. Computers and Mathematics with Applications, 72(4), 952-973. https://doi.org/10.1016/j.camwa.2016.06.001

We present a-posteriori analysis of higher order finite element approximations (hp-FEM) for quadratic Fredholm-valued operator functions. Residual estimates for approximations of the algebraic eigenspaces are derived and we reduce the analysis of the... Read More about Efficient and reliable hp-FEM estimates for quadratic eigenvalue problems and photonic crystal applications.

Two dimensional configurational-force-driven crack propagation using the discontinuous Galerkin method with rp-adaptivity (2016)
Presentation / Conference Contribution
Bird, R., Coombs, W., & Giani, S. (2023, March). Two dimensional configurational-force-driven crack propagation using the discontinuous Galerkin method with rp-adaptivity. Presented at ACME - UK 2016 24th Conference of the Association for Computational Mechanics in Engineering., Cardiff, UK

This paper presents a quasi-static configurational force (CF) brittle fracture propagation method, [1], using the discontinuous Galerkin (dG) symmetric interior penalty (SIP) method, [2]. The method is derived from the first law of thermodynamics wit... Read More about Two dimensional configurational-force-driven crack propagation using the discontinuous Galerkin method with rp-adaptivity.

Topology optimisation using level set methods and the discontinuous Galerkin method (2016)
Presentation / Conference Contribution
Adams, T., Giani, S., & Coombs, W. (2023, March). Topology optimisation using level set methods and the discontinuous Galerkin method. Presented at ACME - UK 2016 24th Conference of the Association for Computational Mechanics in Engineering., Cardiff, UK

This paper presents a topology optimisation approach that combines an adjoint-based sensitivity analysis [1] with level set methods (LSM) [2] for front propagation, and the discontinuous Galerkin (DG) symmetric interior penalty (SIP) method [3]. The... Read More about Topology optimisation using level set methods and the discontinuous Galerkin method.