Inf-sup stable space-time discretization of the wave equation based on a first-order-in-time variational formulation

2025/06/06 by Ferrari, Matteo, Perugia, Ilaria, Zampa, Enrico · 2 citations
#65M60 #65N12 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2506.05886

Abstract

In this paper, we present a conforming space-time discretization of the wave equation based on a first-order-in-time variational formulation with exponential weights in time. We analyze the method, showing its stability without imposing any restrictions on the mesh size or time step, and proving quasi-optimal convergence for any choice of space-time tensor product discrete spaces that satisfies standard approximation assumptions. Numerical examples are provided to support the theoretical findings.

Citations

• Intrinsic unconditional stability in space-time isogeometric approximation of the acoustic wave equation in second-order formulation
• A variational approach to the analysis of the continuous space-time FEM for the wave equation
• Unconditionally stable space-time isogeometric discretization for the wave equation in Hamiltonian formulation
• Stability of conforming space-time isogeometric methods for the wave equation
• A space-time continuous and coercive formulation for the wave equation
• Well-posedness of first-order acoustic wave equations and space-time finite element approximation
• Adaptive least-squares space-time finite element methods
• Numerical results for an unconditionally stable space-time finite element method for the wave equation
• Higher-Order Space-Time Continuous Galerkin Methods for the Wave\n Equation
• Galerkin-collocation approximation in time for the wave equation and its\n post-processing
• Numerical study of Galerkin-collocation approximation in time for the wave equation
• A spacetime DPG method for the Schrodinger equation
• Localized orthogonal decomposition method for the wave equation with a\n continuum of scales
• Continuous finite elements in space and time for the nonhomogeneous wave equation
• A priori and a posteriori error estimates of a \mathcal C⁰-in-time method for the wave equation in second order formulation

Cited by

• Paving the way to a T-coercive method for the wave equation
• Unconditionally stable space-time isogeometric method for the linear Schrödinger equation

Related

• Very Weak Space-Time Variational Formulation for the Wave Equation:\n Analysis and Efficient Numerical Solution
• Numerical results for an unconditionally stable space-time finite element method for the wave equation
• A generalized inf-sup stable variational formulation for the wave\n equation
• Unconditionally stable space-time isogeometric discretization for the wave equation in Hamiltonian formulation
• Higher-Order Space-Time Continuous Galerkin Methods for the Wave\n Equation