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Eliminating Gibbs phenomena: A non-linear Petrov–Galerkin method for the convection–diffusion–reaction equation (2020)
Journal Article
Houston, P., Roggendorf, S., & van der Zee, K. G. (2020). Eliminating Gibbs phenomena: A non-linear Petrov–Galerkin method for the convection–diffusion–reaction equation. Computers and Mathematics with Applications, 80(5), 851-873. https://doi.org/10.1016/j.camwa.2020.03.025

In this article we consider the numerical approximation of the convection-diffusion-reaction equation. One of the main challenges of designing a numerical method for this problem is that boundary layers occurring in the convection-dominated case can... Read More about Eliminating Gibbs phenomena: A non-linear Petrov–Galerkin method for the convection–diffusion–reaction equation.

hp-Adaptive Iterative Linearization Discontinuous-Galerkin FEM for Quasilinear Elliptic Boundary Value Problems (2020)
Conference Proceeding
HOUSTON, P., & WIHLER, T. (2020). hp-Adaptive Iterative Linearization Discontinuous-Galerkin FEM for Quasilinear Elliptic Boundary Value Problems. In S. Sherwin, D. Moxey, J. Peiro, P. Vincent, & C. Schwab (Eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 (407–417). https://doi.org/10.1007/978-3-030-39647-3

In this article we consider the a posteriori error analysis of hp-version discontinuous Galerkin finite element methods for the numerical solution of a second-order quasilinear elliptic boundary value problem of strongly monotone type. In particular,... Read More about hp-Adaptive Iterative Linearization Discontinuous-Galerkin FEM for Quasilinear Elliptic Boundary Value Problems.

An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids (2020)
Journal Article
Antonietti, P. F., Houston, P., Pennesi, G., & Suli, E. (2020). An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids. Mathematics of Computation, 89, 2047-2083 . https://doi.org/10.1090/mcom/3510

In this article we design and analyze a class of two-level non-overlapping additive Schwarz preconditioners for the solution of the linear system of equations stemming from discontinuous Galerkin discretizations of second-order elliptic partial diffe... Read More about An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids.