Abstract
The paper is concerned with functional-type a posteriori estimates for the initial boundary value problem for a parabolic partial differential equation with an obstacle. We deduce a guaranteed and computable bound of the distance between the exact minimizer and any function from the admissible (energy) class of functions. Applications to the analysis of modeling errors caused by data implification are discussed. An important case of time incremental approximations is specially studied. Numerical examples presented in the last section show how the estimates work in practice.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: AP 252/3-1
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 20-01-00397
Funding statement: The first author was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID AP 252/3-1. The paper has also been supported by the RUDN University Strategic Academic Leadership Program. The research of the second author was partially supported by RFBR grant No. 20-01-00397.
Acknowledgements
The authors are indebted to the referees for the valuable remarks.
References
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Articles in the same Issue
- Frontmatter
- A General Error Estimate For Parabolic Variational Inequalities
- Functional A Posteriori Error Estimates for the Parabolic Obstacle Problem
- Multi-Scale Paraxial Models to Approximate Vlasov–Maxwell Equations
- Finite Element Penalty Method for the Oldroyd Model of Order One with Non-smooth Initial Data
- Quasi-Newton Iterative Solution of Non-Orthotropic Elliptic Problems in 3D with Boundary Nonlinearity
- Improving Regularization Techniques for Incompressible Fluid Flows via Defect Correction
- Fully Discrete Finite Element Approximation of the MHD Flow
- Sparse Data-Driven Quadrature Rules via ℓ p -Quasi-Norm Minimization
- Identification of Matrix Diffusion Coefficient in a Parabolic PDE
- A Finite Element Method for Two-Phase Flow with Material Viscous Interface
- On the Finite Element Approximation of Fourth-Order Singularly Perturbed Eigenvalue Problems
- Application of Fourier Truncation Method to Numerical Differentiation for Bivariate Functions
- Factorized Schemes for First and Second Order Evolution Equations with Fractional Powers of Operators
Articles in the same Issue
- Frontmatter
- A General Error Estimate For Parabolic Variational Inequalities
- Functional A Posteriori Error Estimates for the Parabolic Obstacle Problem
- Multi-Scale Paraxial Models to Approximate Vlasov–Maxwell Equations
- Finite Element Penalty Method for the Oldroyd Model of Order One with Non-smooth Initial Data
- Quasi-Newton Iterative Solution of Non-Orthotropic Elliptic Problems in 3D with Boundary Nonlinearity
- Improving Regularization Techniques for Incompressible Fluid Flows via Defect Correction
- Fully Discrete Finite Element Approximation of the MHD Flow
- Sparse Data-Driven Quadrature Rules via ℓ p -Quasi-Norm Minimization
- Identification of Matrix Diffusion Coefficient in a Parabolic PDE
- A Finite Element Method for Two-Phase Flow with Material Viscous Interface
- On the Finite Element Approximation of Fourth-Order Singularly Perturbed Eigenvalue Problems
- Application of Fourier Truncation Method to Numerical Differentiation for Bivariate Functions
- Factorized Schemes for First and Second Order Evolution Equations with Fractional Powers of Operators