Outputs (5)

A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation (2018)
Journal Article
Adams, T., Giani, S., & Coombs, W. (2019). A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation. Journal of Computational Physics, 379, 373-391. https://doi.org/10.1016/j.jcp.2018.12.003

In this paper, an efficient, high-order accurate, level set reinitialisation method is proposed, based on the elliptic reinitialisation method (Basting and Kuzmin, 2013 [1]), which is discretised spatially using the discontinuous Galerkin (DG) symmet... Read More about A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation.

A posteriori discontinuous Galerkin error estimator for linear elasticity (2018)
Journal Article
Bird, R., Coombs, W., & Giani, S. (2019). A posteriori discontinuous Galerkin error estimator for linear elasticity. Applied Mathematics and Computation, 344-345, 78-96. https://doi.org/10.1016/j.amc.2018.08.039

This paper presents for the first time the derivation of an hp a posteriori error estimator for the symmetric interior penalty discontinuous Galerkin finite element method for linear elastic analysis. Any combination of Neumann and Dirichlet boundary... Read More about A posteriori discontinuous Galerkin error estimator for linear elasticity.

hp-adaptive celatus enriched discontinuous Galerkin method for second-order elliptic source problems (2018)
Journal Article
Giani, S. (2018). hp-adaptive celatus enriched discontinuous Galerkin method for second-order elliptic source problems. SIAM Journal on Scientific Computing, 40(5), B1391-B1418. https://doi.org/10.1137/17m1149912

This paper presents a new way to enrich finite element methods with nonpolynomial functions without adding any function to the finite element space. For this reason, the method is called celatus, which is a Latin word meaning ``hidden from view."" Si... Read More about hp-adaptive celatus enriched discontinuous Galerkin method for second-order elliptic source problems.

Reliable anisotropic-adaptive discontinuous Galerkin method for simplified P_N approximations of radiative transfer (2018)
Journal Article
Giani, S. (2018). Reliable anisotropic-adaptive discontinuous Galerkin method for simplified P_N approximations of radiative transfer. Journal of Computational and Applied Mathematics, 337, 225-243. https://doi.org/10.1016/j.cam.2017.12.039

In this paper we present the analysis for the error estimator for radiative transfer problems presented in Giani and Seaid (2016) where we showed the capabilities of the error estimator to accurately drive the adaptivity to resolve steep boundary lay... Read More about Reliable anisotropic-adaptive discontinuous Galerkin method for simplified P_N approximations of radiative transfer.

Earthquake Nucleation Size: Evidence of Loading Rate Dependence in Laboratory Faults (2018)
Journal Article
Guérin‐Marthe, S., Nielsen, S., Bird, R., Giani, S., & Di Toro, G. (2018). Earthquake Nucleation Size: Evidence of Loading Rate Dependence in Laboratory Faults. Journal of Geophysical Research. Solid Earth, 124(1), 689-708. https://doi.org/10.1029/2018jb016803

Recent GPS observations of major earthquakes such as the 2014 Chile megathrust show a slow pre‐slip phase releasing a significant portion of the total moment (Ruiz et al., 2014). Despite advances from theoretical stability analysis (Rubin & Ampuero,... Read More about Earthquake Nucleation Size: Evidence of Loading Rate Dependence in Laboratory Faults.