Peter Monk's contributions to numerical analysis and Maxwell's equations

DOI10.1016/j.camwa.2017.03.023zbMath1397.35003OpenAlexW2604213060MaRDI QIDQ1672622

Ilaria Perugia

Publication date: 11 September 2018

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2017.03.023

zbMATH Keywords

hyperbolic problemswave propagation problems

Mathematics Subject Classification ID

Biographies, obituaries, personalia, bibliographies (01A70) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Electromagnetic theory (general) (78A25) History of partial differential equations (35-03) Maxwell equations (35Q61)

Cites Work

• Unnamed Item
• Error analysis for a hybridizable discontinuous Galerkin method for the Helmholtz equation
• Discretization of the wave equation using continuous elements in time and a hybridizable discontinuous Galerkin method in space
• A discontinuous Galerkin method for linear symmetric hyperbolic systems in inhomogeneous media
• Solving Maxwell's equations using the ultra weak variational formulation
• A finite element method for approximating the time-harmonic Maxwell equations
• A posteriori error indicators for Maxwell's equations
• On the \(p\)- and \(hp\)-extension of Nédélec's curl-conforming elements
• de Rham diagram for \(hp\) finite element spaces
• Maxwell eigenvalues and discrete compactness in two dimensions
• Peter Monk and inverse scattering theory
• Stabilized interior penalty methods for the time-harmonic Maxwell equations.
• Computational aspects of the ultra-weak variational formulation
• Optimizing the perfectly matched layer
• A least-squares method for the Helmholtz equation
• A tent pitching scheme motivated by Friedrichs theory
• An analysis of Nédélec's method for the spatial discretization of Maxwell's equations
• Dispersive and dissipative properties of discontinuous Galerkin finite element methods for the second-order wave equation
• Discrete compactness and the approximation of Maxwell's equations in $\mathbb{R}^3$
• Error estimates for the ultra weak variational formulation in linear elasticity
• Finite element approximation of eigenvalue problems
• Improvements for the ultra weak variational formulation
• A Survey of Trefftz Methods for the Helmholtz Equation
• Finite elements in computational electromagnetism
• Time Domain Integral Equation Methods in Computational Electromagnetism
• Error estimates for the Ultra Weak Variational Formulation of the Helmholtz equation
• A Mixed Method for Approximating Maxwell’s Equations
• Analysis of a Finite Element Method for Maxwell’s Equations
• A Comparison of Three Mixed Methods for the Time-Dependent Maxwell’s Equations
• The Perfectly Matched Layer in Curvilinear Coordinates
• A Dispersion Analysis of Finite Element Methods for Maxwell’s Equations
• Superconvergence of finite element approximations to Maxwell's equations
• The Ultra-Weak Variational Formulation for Elastic Wave Problems
• Finite Element Methods for Maxwell's Equations
• Time-discrete finite element schemes for Maxwell's equations
• A Finite Element/Spectral Method for Approximating the Time-Harmonic Maxwell System in $\mathbb{R}^3 $
• Residual-Based Adaptivity and PWDG Methods for the Helmholtz Equation
• The perfectly matched layer for the ultra weak variational formulation of the 3D Helmholtz equation

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