An \(L^p\)-DPG method for the convection-diffusion problem

DOI10.1016/j.camwa.2020.08.013OpenAlexW3082387576MaRDI QIDQ2034895

Jiaqi Li, Leszek F. Demkowicz

Publication date: 23 June 2021

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2020.08.013

zbMATH Keywords

Banach spacesconvection-dominated diffusionresidual minimizationdiscontinuous Petrov-Galerkin methods

Mathematics Subject Classification ID

Convex programming (90C25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Geometry and structure of normed linear spaces (46B20)

Related Items (7)

Gibbs phenomena for L^q-best approximation in finite element spaces ⋮ An \(L^p\)-DPG method with application to 2D convection-diffusion problems ⋮ Battling Gibbs phenomenon: on finite element approximations of discontinuous solutions of PDEs ⋮ Combining DPG in space with DPG time-marching scheme for the transient advection-reaction equation ⋮ A DPG method for planar div-curl problems ⋮ Editorial: Recent advances in least-squares and discontinuous Petrov-Galerkin finite element methods ⋮ Discretization of Linear Problems in Banach Spaces: Residual Minimization, Nonlinear Petrov--Galerkin, and Monotone Mixed Methods

Cites Work

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• Eliminating Gibbs phenomena: a non-linear Petrov-Galerkin method for the convection-diffusion-reaction equation
• The convection-diffusion-reaction equation in non-Hilbert Sobolev spaces: a direct proof of the inf-sup condition and stability of Galerkin's method
• A robust Petrov-Galerkin discretisation of convection-diffusion equations
• Discretization of Linear Problems in Banach Spaces: Residual Minimization, Nonlinear Petrov--Galerkin, and Monotone Mixed Methods
• An Introduction to Banach Space Theory
• A Finite Element Technique for Solving First-Order PDEs inL^p

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