A DPG-based time-marching scheme for linear hyperbolic problems

DOI10.1016/j.cma.2020.113539zbMath1506.76094OpenAlexW3101901629WikidataQ115578462 ScholiaQ115578462MaRDI QIDQ2020854

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

Publication date: 26 April 2021

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2020.113539

zbMATH Keywords

ODE systemsexponential integratorsoptimal test functionsDPG methodlinear hyperbolic problemsultraweak variational formulation

Mathematics Subject Classification ID

Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (7)

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 ⋮ Automatic variationally stable analysis for finite element computations: transient convection-diffusion problems ⋮ The DPG method for the convection-reaction problem, revisited ⋮ A computational framework for crack propagation along contact interfaces and surfaces under load ⋮ Space-time methods for time-dependent partial differential equations. Abstracts from the workshop held February 6--12, 2022

Uses Software

• Expint
• Algorithm 919
• MATLAB expm
• 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
• Approximate symmetrization and Petrov-Galerkin methods for diffusion- convection problems
• Adaptive Galerkin finite element methods for the wave equation
• Numerical integration of ordinary differential equations based on trigonometric polynomials
• Locally conservative discontinuous Petrov-Galerkin finite elements for fluid problems
• Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms
• 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
• A New Scaling and Squaring Algorithm for the Matrix Exponential
• Exponential Integrators for Large Systems of Differential Equations
• Computing the Wave-Kernel Matrix Functions
• A Truncated Taylor Series Algorithm for Computing the Action of Trigonometric and Hyperbolic Matrix Functions
• A Spacetime DPG Method for the Schrödinger Equation
• New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously
• Exponential Rosenbrock-Type Methods
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• An Overview of the Discontinuous Petrov Galerkin Method
• Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems

This page was built for publication: A DPG-based time-marching scheme for linear hyperbolic problems