A space-time DPG method for the heat equation

DOI10.1016/j.camwa.2021.11.013OpenAlexW3215334222MaRDI QIDQ825502

Lars Diening, Johannes Storn

Publication date: 17 December 2021

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

Full work available at URL: https://arxiv.org/abs/2012.13229

zbMATH Keywords

adaptivityparabolic PDEsDPG methodspace-time FEM

Mathematics Subject Classification ID

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) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

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Cites Work

• Unnamed Item
• Unnamed Item
• Heat equation as a Friedrichs system
• Space-time finite element methods for parabolic problems
• Breaking spaces and forms for the DPG method and applications including Maxwell equations
• A time-stepping DPG scheme for the heat equation
• J.-L. Lions' problem concerning maximal regularity of equations governed by non-autonomous forms
• A class of discontinuous Petrov-Galerkin methods. I: The transport equation
• A stable space-time finite element method for parabolic evolution problems
• An ultraweak formulation of the Reissner-Mindlin plate bending model and DPG approximation
• Analysis of backward Euler primal DPG methods
• An adaptive DPG method for high frequency time-harmonic wave propagation problems
• Space-time least-squares finite elements for parabolic equations
• Time-stepping DPG formulations for the heat equation
• On a relation of discontinuous Petrov-Galerkin and least-squares finite element methods
• Adaptive mesh refinement in 2D -- an efficient implementation in \textsc{Matlab}
• Space-time isogeometric analysis of parabolic evolution problems
• Adaptive strategies for transport equations
• Space-time discontinuous Petrov-Galerkin methods for linear wave equations in heterogeneous media
• Parabolic Lipschitz truncation and caloric approximation
• Error-bounds for finite element method
• Low-order dPG-FEM for an elliptic PDE
• An analysis of the practical DPG method
• Space-time adaptive wavelet methods for parabolic evolution problems
• A class of discontinuous Petrov-Galerkin methods. II. Optimal test functions
• The Skeleton Reduction for Finite Element Substructuring Methods
• 4. A space-time DPG method for the wave equation in multiple dimensions
• On the stability of DPG formulations of transport equations
• An ultraweak formulation of the Kirchhoff–Love plate bending model and DPG approximation
• Stability of sparse space-time finite element discretizations of linear parabolic evolution equations
• Stability of Galerkin discretizations of a mixed space–time variational formulation of parabolic evolution equations
• A Spacetime DPG Method for the Schrödinger Equation
• Further results on a space-time FOSLS formulation of parabolic PDEs
• On the Sobolev and $L^p$-Stability of the $L^2$-Projection
• A Posteriori Error Control for DPG Methods
• Dispersive and Dissipative Errors in the DPG Method with Scaled Norms for Helmholtz Equation
• Discontinuous Galerkin Methods for Friedrichs' Systems. I. General theory