Equivalence between the DPG method and the exponential integrators for linear parabolic problems

DOI10.1016/j.jcp.2020.110016OpenAlexW3110284146WikidataQ115571366 ScholiaQ115571366MaRDI QIDQ2120039

David Pardo, Judit Muñoz-Matute, Leszek F. Demkowicz

Publication date: 31 March 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2020.110016

zbMATH Keywords

ODE systemsexponential integratorsoptimal test functionsDPG methodlinear parabolic problemsultraweak formulation

Mathematics Subject Classification ID

Numerical methods for ordinary differential equations (65Lxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)

Related Items (6)

Analysis of backward Euler primal DPG methods ⋮ Error representation of the time-marching DPG scheme ⋮ Combining DPG in space with DPG time-marching scheme for the transient advection-reaction equation ⋮ A deep double Ritz method (\(\mathrm{D^2RM}\)) for solving partial differential equations using neural networks ⋮ The DPG method for the convection-reaction problem, revisited ⋮ Space-time methods for time-dependent partial differential equations. Abstracts from the workshop held February 6--12, 2022

Uses Software

• Expint
• Algorithm 919
• phipm

Cites Work

• A robust DPG method for convection-dominated diffusion problems. II: Adjoint boundary conditions and mesh-dependent test norms
• A class of discontinuous Petrov-Galerkin methods. III: Adaptivity
• Wavenumber explicit analysis of a DPG method for the multidimensional Helmholtz equation
• Breaking spaces and forms for the DPG method and applications including Maxwell equations
• A time-stepping DPG scheme for the heat equation
• A class of discontinuous Petrov-Galerkin methods. IV: The optimal test norm and time-harmonic wave propagation in 1D
• Exponential multistep methods of Adams-type
• A class of discontinuous Petrov-Galerkin methods. I: The transport equation
• A locking-free \(hp\) DPG method for linear elasticity with symmetric stresses
• An exponential integrator for advection-dominated reactive transport in heterogeneous porous media
• Exponential time integration for fast finite element solutions of some financial engineering problems
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• Approximate symmetrization and Petrov-Galerkin methods for diffusion- convection problems
• Exponential integrators for quantum-classical molecular dynamics
• A massively parallel exponential integrator for advection-diffusion models
• Locally conservative discontinuous Petrov-Galerkin finite elements for fluid problems
• Robust DPG Method for Convection-Dominated Diffusion Problems
• Exponential integrators
• Robust DPG Methods for Transient Convection-Diffusion
• Algorithm 919
• A class of discontinuous Petrov-Galerkin methods. II. Optimal test functions
• Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
• Analysis of the DPG Method for the Poisson Equation
• Adaptive Streamline Diffusion Finite Element Methods for Stationary Convection-Diffusion Problems
• Exponential Integrators for Large Systems of Differential Equations
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• A Spacetime DPG Method for the Schrödinger Equation
• Exponential Rosenbrock-Type Methods
• An Overview of the Discontinuous Petrov Galerkin Method
• Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems

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