An ultraweak space-time variational formulation for the wave equation: Analysis and efficient numerical solution

DOI10.1051/m2an/2022035zbMath1497.35312arXiv2107.12119OpenAlexW4224248463MaRDI QIDQ5867504

Valeria Simoncini, Davide Palitta, Julian Henning, Karsten Urban

Publication date: 14 September 2022

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.12119

zbMATH Keywords

wave equationminimal regularityultraweak formulationnumerical solversoptimal inf-sup stabilitytensor product-style space-time Petrov-Galerkin discretization

Mathematics Subject Classification ID

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) Initial value problems for second-order hyperbolic equations (35L15) Abstract hyperbolic equations (35L90)

Related Items

A space-time variational method for optimal control problems: well-posedness, stability and numerical solution ⋮ Space-time discontinuous Galerkin methods for weak solutions of hyperbolic linear symmetric Friedrichs systems ⋮ An Optimally Stable Approximation of Reactive Transport Using Discrete Test and Infinite Trial Spaces

Uses Software

• redbKIT

Cites Work

• Unnamed Item
• Unnamed Item
• Adaptive rational Krylov subspaces for large-scale dynamical systems
• A new error bound for reduced basis approximation of parabolic partial differential equations
• A priori error analysis of high-order LL* (FOSLL*) finite element methods
• Continuous finite elements in space and time for the nonhomogeneous wave equation
• Some observations on Babuška and Brezzi theories
• A black-box multigrid preconditioner for the biharmonic equation
• Matrix equation techniques for certain evolutionary partial differential equations
• A generalized inf-sup stable variational formulation for the wave equation
• Space-time discontinuous Petrov-Galerkin methods for linear wave equations in heterogeneous media
• Discretization of the Poisson equation with non-smooth data and emphasis on non-convex domains
• Error Analysis for a Finite Element Approximation of Elliptic Dirichlet Boundary Control Problems
• Certified Reduced Basis Methods for Parametrized Partial Differential Equations
• An Efficient Reduced Basis Solver for Stochastic Galerkin Matrix Equations
• Robust DPG Methods for Transient Convection-Diffusion
• A class of discontinuous Petrov-Galerkin methods. II. Optimal test functions
• Computational Methods for Linear Matrix Equations
• Low-Rank Tensor Krylov Subspace Methods for Parametrized Linear Systems
• The Newmark Method and a Space–Time FEM for the Second–Order Wave Equation
• Theory of adaptive finite element methods: An introduction
• Analysis of Mixed Methods Using Mesh Dependent Norms
• Negative Norm Estimates for Fully Discrete Finite Element Approximations to the Wave Equation with Nonhomogeneous L 2 Dirichlet Boundary Data
• (Parametrized) First Order Transport Equations: Realization of Optimally Stable Petrov--Galerkin Methods
• Approximations of Very Weak Solutions to Boundary-Value Problems
• Adaptive Petrov--Galerkin Methods for First Order Transport Equations
• Stability of sparse space-time finite element discretizations of linear parabolic evolution equations
• A Spacetime DPG Method for the Schrödinger Equation
• Matrix Oriented Reduction of Space-Time Petrov-Galerkin Variational Problems
• Constructively well-posed approximation methods with unity inf–sup and continuity constants for partial differential equations
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• An improved error bound for reduced basis approximation of linear parabolic problems
• Reduced Basis Methods for Partial Differential Equations