Design and performance of a space-time virtual element method for the heat equation on prismatic meshes

DOI10.1016/j.cma.2023.116491arXiv2306.09191OpenAlexW4387397548MaRDI QIDQ6118550

Lorenzo Mascotto, Sergio Gómez, Ilaria Perugia

Publication date: 21 March 2024

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

Full work available at URL: https://arxiv.org/abs/2306.09191

zbMATH Keywords

heat equationspace-time methodsvirtual element methodspolytopic meshes

Mathematics Subject Classification ID

Heat equation (35K05) 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)

Cites Work

• Unnamed Item
• Space-time finite element methods for parabolic problems
• Space-time discontinuous Galerkin method for advection-diffusion problems on time-dependent domains
• A posteriori error estimates for the virtual element method
• Coercive space-time finite element methods for initial boundary value problems
• Space-time least-squares finite elements for parabolic equations
• Numerical results for adaptive (negative norm) constrained first order system least squares formulations
• Space-time isogeometric analysis of parabolic evolution problems
• Space-time discretizations using constrained first-order system least squares (CFOSLS)
• A space-time formulation for multiscale phenomena
• Space-time adaptive wavelet methods for parabolic evolution problems
• 7. Space-time finite element methods for parabolic evolution equations: discretization, a posteriori error estimation, adaptivity and solution
• The h-p version of the finite element method for parabolic equations. Part I. The p-version in time
• Time discretization of parabolic problems by the discontinuous Galerkin method
• Continuous Finite Elements in Space and Time for the Heat Equation
• Galerkin-Type Approximations which are Discontinuous in Time for Parabolic Equations in a Variable Domain
• Time Discretization of Parabolic Problems by the HP-Version of the Discontinuous Galerkin Finite Element Method
• Comparison of algebraic multigrid methods for an adaptive space–time finite‐element discretization of the heat equation in 3D and 4D
• A continuous space-time finite element method for the wave equation
• A Convergent Adaptive Algorithm for Poisson’s Equation
• Stability of Galerkin discretizations of a mixed space–time variational formulation of parabolic evolution equations
• Further results on a space-time FOSLS formulation of parabolic PDEs
• The h‐p version of the finite element method for parabolic equations. II. The h‐p version in time
• Space–time least–squares isogeometric method and efficient solver for parabolic problems
• $hp$-Version Space-Time Discontinuous Galerkin Methods for Parabolic Problems on Prismatic Meshes