Multistage discontinuous Petrov-Galerkin time-marching scheme for nonlinear problems

DOI10.1137/23m1598088zbMath1545.65312MaRDI QIDQ6590543

Judit Muñoz-Matute, L. Demkowicz

Publication date: 21 August 2024

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

nonlinear problemsoptimal test functionsultraweak formulationexponential Rosenbrock integratorshybrid Euler methodmultistage DPG method

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Cites Work

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• The DPG method for the Stokes problem
• Nonlinear stability of the implicit-explicit methods for the Allen-Cahn equation
• 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
• Generalized integrating factor methods for stiff PDEs
• A class of explicit multistep exponential integrators for semilinear problems
• Implementation of exponential Rosenbrock-type integrators
• Exponential Runge-Kutta methods for parabolic problems.
• A DPG-based time-marching scheme for linear hyperbolic problems
• Equivalence between the DPG method and the exponential integrators for linear parabolic problems
• Exponential Rosenbrock methods of order five -- construction, analysis and numerical comparisons
• Explicit exponential Runge-Kutta methods of high order for parabolic problems
• Adaptive Galerkin finite element methods for the wave equation
• Error representation of the time-marching DPG scheme
• Combining DPG in space with DPG time-marching scheme for the transient advection-reaction equation
• Robust DPG Method for Convection-Dominated Diffusion Problems
• Exponential integrators
• 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
• A Spacetime DPG Method for the Schrödinger Equation
• Exponential Rosenbrock-Type Methods
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• An Overview of the Discontinuous Petrov Galerkin Method
• Energy properties preserving schemes for Burgers' equation
• Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems
• A Lawson-type exponential integrator for the Korteweg–de Vries equation

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