Conforming and nonconforming finite element methods for biharmonic inverse source problem

DOI10.1088/1361-6420/ac3ec5zbMath1493.65181arXiv2106.07357OpenAlexW3217623183MaRDI QIDQ5019924

Devika Shylaja, M. Thamban Nair

Publication date: 11 January 2022

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.07357

zbMATH Keywords

error estimatesfinite element methodsTikhonov regularizationinverse source problembiharmonic problem

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Ill-posed problems for PDEs (35R25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (1)

Conforming VEM for general second-order elliptic problems with rough data on polygonal meshes and its application to a Poisson inverse source problem

Cites Work

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• \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
• Finite element approximation of the Navier-Stokes equations
• Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
• The Hessian discretisation method for fourth order linear elliptic equations
• A Morley finite element method for the displacement obstacle problem of clamped Kirchhoff plates
• Morley FEM for a distributed optimal control problem governed by the von Kármán equations
• A discrete Helmholtz decomposition with morley finite element functions and the optimality of adaptive finite element schemes
• A priori error estimate of the finite element solution to a Poisson inverse source problem
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Morley finite element method for the eigenvalues of the biharmonic operator
• A family of $C^1$ finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems
• On the boundary value problem of the biharmonic operator on domains with angular corners
• A Priori Error Analysis for the hp-Version of the Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
• Nonconforming finite element discretization for semilinear problems with trilinear nonlinearity
• How to Prove the Discrete Reliability for Nonconforming Finite Element Methods
• Morley finite element method for the von Kármán obstacle problem
• Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems
• Improved L² and H¹ error estimates for the Hessian discretization method

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