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Quantifying simulator discrepancy in discrete-time dynamical simulators (2011)
Journal Article
Wilkinson, R. D., Vrettas, M., Cornford, D., & Oakley, J. E. Quantifying simulator discrepancy in discrete-time dynamical simulators. Manuscript submitted for publication

When making predictions with complex simulators it can be important to quantify the various sources of uncertainty. Errors in the structural specification of the simulator, for example due to missing processes or incorrect mathematical specification... Read More about Quantifying simulator discrepancy in discrete-time dynamical simulators.

Discontinuous Galerkin methods for problems with Dirac delta source (2011)
Journal Article
Houston, P., & Wihler, T. P. Discontinuous Galerkin methods for problems with Dirac delta source. Manuscript submitted for publication

In this article we study discontinuous Galerkin finite element discretizations of linear second-order elliptic partial differential equations with Dirac delta right-hand side. In particular, assuming that the underlying computational mesh is quasi-un... Read More about Discontinuous Galerkin methods for problems with Dirac delta source.

Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows (2011)
Journal Article
Giani, S., & Houston, P. Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows. Manuscript submitted for publication

In this article we consider the construction of general isotropic and anisotropic adaptive mesh refinement strategies, as well as hp-mesh refinement techniques, for the numerical approximation of the compressible Euler and Navier-Stokes equations. To... Read More about Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows.

An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems (2011)
Journal Article
Giani, S., & Hall, E. An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems. Manuscript submitted for publication

In this paper we present a residual-based {\em a posteriori} error estimator for $hp$-adaptive discontinuous Galerkin (DG) methods for elliptic eigenvalue problems. In particular we use as a model problem the Laplace eigenvalue problem on bounded dom... Read More about An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems.

A second-order class-D audio amplifier (2011)
Journal Article
Cox, S. M., Tan, M., & Yu, J. (2011). A second-order class-D audio amplifier. SIAM Journal on Applied Mathematics, 71(1), https://doi.org/10.1137/100788367

Class-D audio amplifiers are particularly efficient, and this efficiency has led to their ubiquity in a wide range of modern electronic appliances. Their output takes the form of a high-frequency square wave whose duty cycle (ratio of on-time to off-... Read More about A second-order class-D audio amplifier.

Benchmark results for testing adaptive finite element eigenvalue procedures (2011)
Journal Article
Giani, S., Grubišić, L., & Ovall, J. Benchmark results for testing adaptive finite element eigenvalue procedures. Manuscript submitted for publication

A discontinuous Galerkin method, with hp-adaptivity based on the approximate solution of appropriate dual problems, is employed for highly-accurate eigenvalue
computations on a collection of benchmark examples. After demonstrating the effectivity... Read More about Benchmark results for testing adaptive finite element eigenvalue procedures.

An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for computing band gaps in photonic crystals (2011)
Journal Article
Giani, S. An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for computing band gaps in photonic crystals. Manuscript submitted for publication

In this paper we propose and analyze a hp-adaptive discontinuous finite element
method for computing the band structure of 2D periodic photonic crystals. The
problem can be reduced to the computation of the discrete spectrum of each member in a f... Read More about An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for computing band gaps in photonic crystals.

Cardiac cell modelling: observations from the heart of the cardiac physiome project (2011)
Journal Article
Fink, M., Niederer, S. A., Cherry, E. M., Fenton, F. H., Koivumäki, J. T., Seemann, G., Thul, R., Zhang, H., Sachse, F. B., Beard, D., Crampin, E. J., & Smith, N. P. (2011). Cardiac cell modelling: observations from the heart of the cardiac physiome project. Progress in Biophysics and Molecular Biology, 104(1-3), https://doi.org/10.1016/j.pbiomolbio.2010.03.002

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In... Read More about Cardiac cell modelling: observations from the heart of the cardiac physiome project.

Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs (2011)
Journal Article
Congreve, S., Houston, P., & Wihler, T. P. (2011). Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs. PAMM, 11(1), https://doi.org/10.1002/pamm.201110002

In this article we develop the a priori error analysis of so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical approximation of strongly monotone second-order quasilinear partial differential equations. In thi... Read More about Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs.