Construction of DPG Fortin operators revisited

DOI10.1016/j.camwa.2020.07.020zbMath1458.65146OpenAlexW3049483299MaRDI QIDQ2214416

Pietro Zanotti, Leszek F. Demkowicz

Publication date: 8 December 2020

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2020.07.020

zbMATH Keywords

Fortin operatorDPG methodultraweak variational formulationaffine tetrahedral elementexact energy space

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items (8)

A stable space-time FE method for the shallow water equations ⋮ A stable FE method for the space-time solution of the Cahn-Hilliard equation ⋮ An \(L^p\)-DPG method with application to 2D convection-diffusion problems ⋮ Robust DPG Test Spaces and Fortin Operators—The \(\boldsymbol{H^1}\) and \({\boldsymbol{H}}\boldsymbol{(\mathrm{div})}\) Cases ⋮ Automatic variationally stable analysis for finite element computations: transient convection-diffusion problems ⋮ The DPG method for the convection-reaction problem, revisited ⋮ A DPG method for planar div-curl problems ⋮ Discretization of Linear Problems in Banach Spaces: Residual Minimization, Nonlinear Petrov--Galerkin, and Monotone Mixed Methods

Cites Work

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• Breaking spaces and forms for the DPG method and applications including Maxwell equations
• Mixed finite elements in \(\mathbb{R}^3\)
• Construction of DPG Fortin operators for second order problems
• Fully discrete DPG methods for the Kirchhoff-Love plate bending model
• Adaptivity and variational stabilization for convection-diffusion equations
• An analysis of the practical DPG method
• A class of discontinuous Petrov-Galerkin methods. II. Optimal test functions
• Mixed Finite Element Methods and Applications
• Applied Functional Analysis, Third Edition
• Low-Order Discontinuous Petrov--Galerkin Finite Element Methods for Linear Elasticity

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