An Elementary Method of Deriving A Posteriori Error Equalities and Estimates for Linear Partial Differential Equations
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Immanuel Anjam
und
Dirk Pauly
Abstract
In this paper we present a simple method of deriving a posteriori error equalities and estimates for linear elliptic and parabolic partial differential equations. The error is measured in a combined norm taking into account both the primal and dual variables. We work only on the continuous (often called functional) level and do not suppose any specific properties of numerical methods and discretizations.
References
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Presentation of the Special Issue on Recent Advances in PDE: Theory, Computations and Applications
- Higher Order Mixed FEM for the Obstacle Problem of the p-Laplace Equation Using Biorthogonal Systems
- Edge Patch-Wise Local Projection Stabilized Nonconforming FEM for the Oseen Problem
- Multigrid Methods Based on Hodge Decomposition for a Quad-Curl Problem
- Quasi-Optimality of Adaptive Mixed FEMs for Non-selfadjoint Indefinite Second-Order Linear Elliptic Problems
- Analysis of FEAST Spectral Approximations Using the DPG Discretization
- Stabilizability of Infinite Dimensional Systems by Finite Dimensional Control
- An Explicit-Implicit Splitting Method for a Convection-Diffusion Problem
- Positivity Preserving Gradient Approximation with Linear Finite Elements
- An Elementary Method of Deriving A Posteriori Error Equalities and Estimates for Linear Partial Differential Equations
- Estimation of the Time-Dependent Body Force Needed to Exert on a Membrane to Reach a Desired State at the Final Time
- Mixed Schemes for Fourth-Order DIV Equations
- Improved Analysis and Simulation of a Time-Domain Carpet Cloak Model
- The Boundary Effect in the Accuracy Estimate for the Grid Solution of the Fractional Differential Equation
Artikel in diesem Heft
- Frontmatter
- Presentation of the Special Issue on Recent Advances in PDE: Theory, Computations and Applications
- Higher Order Mixed FEM for the Obstacle Problem of the p-Laplace Equation Using Biorthogonal Systems
- Edge Patch-Wise Local Projection Stabilized Nonconforming FEM for the Oseen Problem
- Multigrid Methods Based on Hodge Decomposition for a Quad-Curl Problem
- Quasi-Optimality of Adaptive Mixed FEMs for Non-selfadjoint Indefinite Second-Order Linear Elliptic Problems
- Analysis of FEAST Spectral Approximations Using the DPG Discretization
- Stabilizability of Infinite Dimensional Systems by Finite Dimensional Control
- An Explicit-Implicit Splitting Method for a Convection-Diffusion Problem
- Positivity Preserving Gradient Approximation with Linear Finite Elements
- An Elementary Method of Deriving A Posteriori Error Equalities and Estimates for Linear Partial Differential Equations
- Estimation of the Time-Dependent Body Force Needed to Exert on a Membrane to Reach a Desired State at the Final Time
- Mixed Schemes for Fourth-Order DIV Equations
- Improved Analysis and Simulation of a Time-Domain Carpet Cloak Model
- The Boundary Effect in the Accuracy Estimate for the Grid Solution of the Fractional Differential Equation
