Nonlinear discontinuous Petrov-Galerkin methods

DOI10.1007/s00211-018-0947-5zbMath1398.65292arXiv1710.00529OpenAlexW2963343145MaRDI QIDQ1651002

Carsten Carstensen, Friederike Hellwig, Philipp Bringmann, Peter Wriggers

Publication date: 16 July 2018

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.00529

zbMATH Keywords

a priori estimatesmixed formulationdiscontinuous Petrov-Galerkin methoddiscrete minimizerseduced formulationnonlinear uniformly convex model

Mathematics Subject Classification ID

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)

Related Items (11)

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 ⋮ Adaptive Least-Squares, Discontinuous Petrov-Galerkin, and Hybrid High-Order Methods ⋮ On a relation of discontinuous Petrov-Galerkin and least-squares finite element methods ⋮ A DPG Framework for Strongly Monotone Operators ⋮ An Adaptive Discontinuous Petrov--Galerkin Method for the Grad--Shafranov Equation ⋮ Optimal Convergence Rates for Adaptive Lowest-Order Discontinuous Petrov--Galerkin Schemes ⋮ An unconditionally stable space-time FE method for the Korteweg-de Vries equation ⋮ Discretization of Linear Problems in Banach Spaces: Residual Minimization, Nonlinear Petrov--Galerkin, and Monotone Mixed Methods ⋮ Goal-Oriented Adaptive Mesh Refinement for Discontinuous Petrov--Galerkin Methods ⋮ The discrete-dual minimal-residual method (DDMRES) for weak advection-reaction problems in Banach spaces

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