P
Paul Houston
Researcher at University of Nottingham
Publications - 141
Citations - 6107
Paul Houston is an academic researcher from University of Nottingham. The author has contributed to research in topics: Discontinuous Galerkin method & Finite element method. The author has an hindex of 44, co-authored 141 publications receiving 5581 citations. Previous affiliations of Paul Houston include University of Leicester & University of Oxford.
Papers
More filters
Journal ArticleDOI
Discontinuous hp -Finite Element Methods for Advection-Diffusion-Reaction Problems
TL;DR: The hp-version of the discontinuous Galerkin finite element method for second-order partial differential equations with nonnegative characteristic form is considered, and an hp-optimal error bound is derived in the hyperbolic case and in the self-adjoint elliptic case.
Journal ArticleDOI
Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations
Ralf Hartmann,Paul Houston +1 more
TL;DR: An approach for the design of adaptive discontinuous Galerkin finite element methods is applied to physically relevant problems arising in inviscid compressible fluid flows governed by the Euler equations of gas dynamics, providing reliable and efficient error estimation.
Book
hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes
TL;DR: An hp-version interior penalty discontinuous Galerkin method (DGFEM) for the numerical solution of second-order elliptic partial differential equations on general computational meshes consisting of polygonal/polyhedral elements is presented and analysed.
Journal ArticleDOI
Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws
Ralf Hartmann,Paul Houston +1 more
TL;DR: This work considers the a posteriori error analysis and adaptive mesh design for discontinuous Galerkin finite element approximations to systems of nonlinear hyperbolic conservation laws and demonstrates the superiority of this approach over standard mesh refinement algorithms which employ Type II error indicators.
Journal ArticleDOI
ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS
TL;DR: This paper develops the a posteriori error estimation of hp-version interior penalty discontinuous Galerkin discretizations of elliptic boundary-value problems and derivesable upper and lower bounds on the error measured in terms of a natural energy norm.