Time-stepping DPG formulations for the heat equation

DOI10.1016/j.camwa.2020.05.024OpenAlexW3037533100WikidataQ115099871 ScholiaQ115099871MaRDI QIDQ2034901

S. Henneking, Nathan V. Roberts

Publication date: 23 June 2021

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

Full work available at URL: https://www.osti.gov/biblio/1667435

zbMATH Keywords

heat equationRothe's methodtime discretizationtransient problemDPG method

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)

Related Items (7)

Analysis of backward Euler primal DPG methods ⋮ A space-time DPG method for the heat equation ⋮ Error representation of the time-marching DPG scheme ⋮ Combining DPG in space with DPG time-marching scheme for the transient advection-reaction equation ⋮ An implicit-in-time DPG formulation of the 1D1V Vlasov-Poisson equations ⋮ Space-time methods for time-dependent partial differential equations. Abstracts from the workshop held February 6--12, 2022 ⋮ Editorial: Recent advances in least-squares and discontinuous Petrov-Galerkin finite element methods

Uses Software

• Camellia

Cites Work

• Breaking spaces and forms for the DPG method and applications including Maxwell equations
• A time-stepping DPG scheme for the heat equation
• Construction of DPG Fortin operators for second order problems
• Space-time discontinuous Petrov-Galerkin methods for linear wave equations in heterogeneous media
• Camellia: a rapid development framework for finite element solvers
• Error-bounds for finite element method
• Adaptivity and variational stabilization for convection-diffusion equations
• An analysis of the practical DPG method
• 4. A space-time DPG method for the wave equation in multiple dimensions
• A Spacetime DPG Method for the Schrödinger Equation

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