Analysis of Lavrentiev-finite element methods for data completion problems
DOI10.1007/s00211-017-0930-6zbMath1444.65035OpenAlexW2770696325MaRDI QIDQ1749435
Vivette Girault, Faker Ben Belgacem, Faten Jelassi
Publication date: 16 May 2018
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00211-017-0930-6
Cauchy problemill-posednessvariational frameworksemi-discrete problembias-variance errorLavrentiev-finite element method
Ill-posedness and regularization problems in numerical linear algebra (65F22) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of inverse problems involving ordinary differential equations (65L09)
Related Items (4)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Local convergence of the Lavrentiev method for the Cauchy problem via a Carleman inequality
- Numerical analysis of an energy-like minimization method to solve the Cauchy problem with noisy data
- The method of fundamental solutions for the Cauchy problem in two-dimensional linear elasticity
- Method of fundamental solutions with optimal regularization techniques for the Cauchy problem of the Laplace equation with singular points
- Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
- Variational discretization of elliptic boundary value problems.
- The inhomogeneous Dirichlet problem in Lipschitz domains
- A priori estimates of Carleman's type in domains with boundary
- On the determination of missing boundary data for solids with nonlinear material behaviors, using displacement fields measured on a part of their boundaries
- Carleman estimates for the regularization of ill-posed Cauchy problems
- On the \(H^1\)-stability of the \(L_2\)-projection onto finite element spaces
- On the stability of the $L^2$ projection in $H^1(\Omega)$
- Two-grid finite-element schemes for the transient Navier-Stokes problem
- A coupled complex boundary method for the Cauchy problem
- An $H_\mathsf{div}$-Based Mixed Quasi-reversibility Method for Solving Elliptic Cauchy Problems
- Analysis of the Scott–Zhang interpolation in the fractional order Sobolev spaces
- A finite element model for the data completion problem: analysis and assessment
- On Cauchy's problem: I. A variational Steklov–Poincaré theory
- Why is the Cauchy problem severely ill-posed?
- Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
- The Lavrentiev regularization of the data completion problem
- A Carleman estimate and the balancing principle in the quasi-reversibility method for solving the Cauchy problem for the Laplace equation
- Determining conductivity by boundary measurements II. Interior results
- The $h-p$ version of the finite element method with quasiuniform meshes
- The Stability in L p and W p 1 of the L 2 -Projection onto Finite Element Function Spaces
- The Neumann problem on Lipschitz domains
- Interior Estimates for Ritz-Galerkin Methods
- A duality-based method of quasi-reversibility to solve the Cauchy problem in the presence of noisy data
- A convergent data completion algorithm using surface integral equations
- Convergence rates for the quasi-reversibility method to solve the Cauchy problem for Laplace's equation
- Solving a Cauchy problem for a 3D elliptic PDE with variable coefficients by a quasi-boundary-value method
- On Cauchy's problem: II. Completion, regularization and approximation
- Inverse problems for partial differential equations
This page was built for publication: Analysis of Lavrentiev-finite element methods for data completion problems
