Stabilised Finite Element Methods for Ill-Posed Problems with Conditional Stability

DOI10.1007/978-3-319-41640-3_4zbMath1357.65254arXiv1512.02837OpenAlexW2291219070MaRDI QIDQ2963090

Erik Burman

Publication date: 10 February 2017

Published in: Lecture Notes in Computational Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.02837

zbMATH Keywords

stabilityerror estimatesnumerical examplesfinite element methodsill-posed problemselliptic Cauchy problem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) 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) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (9)

Primal-Dual Mixed Finite Element Methods for the Elliptic Cauchy Problem ⋮ Least squares solvers for ill-posed PDEs that are conditionally stable ⋮ Data assimilation finite element method for the linearized Navier–Stokes equations in the low Reynolds regime ⋮ Fully discrete finite element data assimilation method for the heat equation ⋮ A Nonlinear Finite Volume Element Method Satisfying Maximum Principle for Anisotropic Diffusion Problems on Arbitrary Triangular Meshes ⋮ Unique continuation for the Helmholtz equation using stabilized finite element methods ⋮ Low regularity primal-dual weak Galerkin finite element methods for convection-diffusion equations ⋮ Primal Dual Mixed Finite Element Methods for Indefinite Advection-Diffusion Equations ⋮ The “Exterior Approach" Applied to the Inverse Obstacle Problem for the Heat Equation

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