The Cauchy problem for Laplace's equation via a modified conjugate gradient method and energy space approaches

DOI10.1002/mma.8710MaRDI QIDQ6182934

Saber Amdouni, Amel Ben Abda

Publication date: 22 December 2023

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

finite element methodCauchy problemconjugate gradient methodLaplace problemenergy space approaches

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Cites Work

• An iterative boundary element method for Cauchy inverse problems
• Solution of the Cauchy problem using iterated Tikhonov regularization
• A Variational Method and Approximations of a Cauchy Problem for Elliptic Equations
• On Cauchy's problem: I. A variational Steklov–Poincaré theory
• Solving Cauchy problems by minimizing an energy-like functional
• The Cauchy problem for Laplace's equation via the conjugate gradient method
• A mixed formulation of the Tikhonov regularization and its application to inverse PDE problems
• Convergence of an Alternating Method to Solve the Cauchy Problem for Poisson's Equation
• A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation
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