Finite Element Collocation Methods for First Order Systems

DOI10.2307/2006067zbMath0417.65056OpenAlexW4240110314MaRDI QIDQ3208033

Pierre-Arnaud Raviart, Pierre Lesaint

Publication date: 1979

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2006067

zbMATH Keywords

stabilityheat equationerror estimatesfinite element methodscollocation methodsnoncylindrical domainfirst-order hyperbolic systemsneutron transport equationnonrectangle meshes

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Initial-boundary value problems for first-order hyperbolic systems (35L50)

Related Items (29)

Discontinuous finite elements and Godunov-type methods for the Eulerian equations of gas dynamics ⋮ On the stability and performance of the \(p\)-version of the finite element method for first-order hyperbolic problems ⋮ A space-time formulation and improved spatial reconstruction for the ``divide-and-conquer multiscale method ⋮ Analysis of the hybrid finite element/finite volume methods for linear hyperbolic and convection-dominated convection-diffusion problems ⋮ Nonuniform time-step Runge-Kutta discontinuous Galerkin method for computational aeroacoustics ⋮ A weakly penalized discontinuous Galerkin method for radiation in dense, scattering media ⋮ A multiscale discontinuous Galerkin method with the computational structure of a continuous Galerkin method ⋮ On direct methods for the discretization of a heat-conduction equation using spline functions ⋮ Finite element methods for linear hyperbolic problems ⋮ Approximation of a diffusion-convection equation by a mixed finite element method: Application to the water flooding problem ⋮ Error estimates for the hybrid finite element/finite volume methods for linear hyperbolic and convection-dominated problems ⋮ Continuous and discontinuous finite element methods for Burgers' equation ⋮ A local discontinuous Galerkin method for the second-order wave equation ⋮ Coupled discontinuous and continuous Galerkin finite element methods for the depth-integrated shallow water equations. ⋮ Comparison of some finite element methods for solving the diffusion-convection-reaction equation ⋮ Implementation and adaptivity of a space-time finite element method for structural dynamics ⋮ The asymptotic diffusion limit of a linear discontinuous discretization of a two-dimensional linear transport equation ⋮ A Finite Difference Method for Symmetric Positive Differential Equations ⋮ Analysis of a numerical solver for radiative transport equation ⋮ Nonconforming finite element approximation of the Giesekus model for polymer flows ⋮ Numerical solutions of the Eulerian equations of compressible flow by a finite element method which follows the free boundary and the interfaces ⋮ Computing reactive flows with a field Monte Carlo formulation and multi-scale methods ⋮ A subdomain residual method for a posteriori error estimates of finite element solutions of viscoelastic fluid flows ⋮ A discontinuous \(hp\) finite element method for convection-diffusion problems ⋮ Fourier analysis of semi-discrete and space--time stabilized methods for the advective--diffusive--reactive equation: II. SGS ⋮ Fourier analysis of semi-discrete and space--time stabilized methods for the advective--diffusive--reactive equation. I: SUPG ⋮ Discontinuous upwinding and mixed finite elements for two-phase flows in reservoir simulation ⋮ Continuous Finite Elements in Space and Time for the Heat Equation ⋮ Simulation of a viscous compressible flow past a circular cylinder with high-order discontinuous Galerkin methods

This page was built for publication: Finite Element Collocation Methods for First Order Systems