Second order approximations for kinetic and potential energies in Maxwell's wave equations

DOI10.1016/j.apnum.2017.05.005zbMath1372.78016OpenAlexW2616479527MaRDI QIDQ2012623

L. Pinto, D. Jordão, José Augusto Ferreira

Publication date: 1 August 2017

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10316/45375

zbMATH Keywords

finite element methodfinite difference methodMaxwell equationssuperclosenesssupraconvergenceenhanced drug delivery

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite difference methods applied to problems in optics and electromagnetic theory (78M20) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Waves and radiation in optics and electromagnetic theory (78A40)

Related Items

Nonlinear systems of parabolic IBVP: a stable super-supraconvergent fully discrete piecewise linear FEM ⋮ Approximating coupled hyperbolic-parabolic systems arising in enhanced drug delivery ⋮ Numerical analysis of a porous-elastic model for convection enhanced drug delivery ⋮ Drug delivery enhanced by ultrasound: mathematical modeling and simulation ⋮ A numerical scheme for a partial differential system motivated by light-triggered drug delivery

Cites Work

• Unnamed Item
• Unnamed Item
• Superconvergence analysis of Yee scheme for metamaterial Maxwell's equations on non-uniform rectangular meshes
• Transdermal transport pathway creation: electroporation pulse order
• A discontinuous Galerkin method for linear symmetric hyperbolic systems in inhomogeneous media
• \(H^{1}\)-second order convergent estimates for non-Fickian models
• A priori estimates for mixed finite element methods for the wave equation
• Convergence of method of lines approximations to partial differential equations
• A singular perturbation of the heat equation with memory
• Mass transfer model for drug delivery in tissue cells with reversible electroporation
• Finite element approximation of the hyperbolic wave equation in mixed form
• Discontinuous Galerkin finite element methods for second order hyperbolic problems
• A second order approximation for quasilinear non-Fickian diffusion models
• Supraconvergence and supercloseness in Volterra equations
• Superconvergence of mixed finite element semi-discretizations of two time-dependent problems.
• Supraconvergence and supercloseness in quasilinear coupled problems
• Error Estimates for Finite Element Methods for Second Order Hyperbolic Equations
• A Convergence Analysis of Yee’s Scheme on Nonuniform Grids
• Superconvergence of finite element approximations to Maxwell's equations
• A Priori Error Estimates for Mixed Finite Element Approximations of the Acoustic Wave Equation
• Interior Maximum-Norm Estimates for Finite Element Methods, Part II
• Construction Analysis of Fourth-Order Finite Difference Schemes for the Acoustic Wave Equation in Nonhomogeneous Media
• Superconvergence of the local discontinuous galerkin method applied to the one‐dimensional second‐order wave equation
• Superconvergence analysis for Maxwell's equations in dispersive media
• Supraconvergence and Supercloseness of a Scheme for Elliptic Equations on Nonuniform Grids
• Estimation of Linear Functionals on Sobolev Spaces with Application to Fourier Transforms and Spline Interpolation
• $L^2 $-Estimates for Galerkin Methods for Second Order Hyperbolic Equations
• Supraconvergence of a finite difference scheme for solutions in Hs(0, L)