A Hybridized High-Order Method for Unique Continuation Subject to the Helmholtz Equation
DOI10.1137/20M1375619zbMath1481.65207OpenAlexW3095703632MaRDI QIDQ5157401
Erik Burman, Guillaume Delay, Alexandre Ern
Publication date: 18 October 2021
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/20m1375619
error analysisunique continuationill-posed problemdiscontinuous GalerkinHelmholtz problemhybridized scheme
Error bounds for boundary value problems involving PDEs (65N15) Ill-posed problems for PDEs (35R25) 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) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)
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Cites Work
- Unnamed Item
- Unnamed Item
- Error estimates for stabilized finite element methods applied to ill-posed problems
- An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators
- Implementation of discontinuous skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming
- A hybrid high-order locking-free method for linear elasticity on general meshes
- Primal-dual weak Galerkin finite element methods for elliptic Cauchy problems
- Unique continuation for the Helmholtz equation using stabilized finite element methods
- A new primal-dual weak Galerkin finite element method for ill-posed elliptic Cauchy problems
- A stabilized finite element method for inverse problems subject to the convection-diffusion equation. I: Diffusion-dominated regime
- High order exactly divergence-free Hybrid Discontinuous Galerkin methods for unsteady incompressible flows
- A stabilized nonconforming finite element method for the elliptic Cauchy problem
- An $H_\mathsf{div}$-Based Mixed Quasi-reversibility Method for Solving Elliptic Cauchy Problems
- Inverse Problems
- Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation
- Increased stability in the continuation of solutions to the Helmholtz equation
- Continuous dependence on data for solutions of partial differential equations with a prescribed bound
- Continuous interior penalty $hp$-finite element methods for advection and advection-diffusion equations
- Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
- The stability for the Cauchy problem for elliptic equations
- Théorème d'unicité adapté au contrôle des solutions des problèmes hyperboliques
- Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization
- Space time stabilized finite element methods for a unique continuation problem subject to the wave equation
- Finite Elements I
- Convergence rates for the quasi-reversibility method to solve the Cauchy problem for Laplace's equation
- Stabilized Finite Element Methods for Nonsymmetric, Noncoercive, and Ill-Posed Problems. Part I: Elliptic Equations
- A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation
- Inverse problems for partial differential equations
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