A New Mixed Functional-probabilistic Approach for Finite Element Accuracy
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Joël Chaskalovic
Abstract
The aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble–Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements
Acknowledgements
The authors want to warmly dedicate this research to pay homage to the memory of Professors André Avez and Gérard Tronel who largely promote the passion of research and teaching in mathematics.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Editorial
- Modern Problems of Numerical Analysis. On the Centenary of the Birth of Alexander Andreevich Samarskii
- Special Issue Articles
- Finite Difference Approximation of a Generalized Time-Fractional Telegraph Equation
- Weighted Estimates for Boundary Value Problems with Fractional Derivatives
- Lagrangian Mixed Finite Element Methods for Nonlinear Thin Shell Problems
- Reliable Computer Simulation Methods for Electrostatic Biomolecular Models Based on the Poisson–Boltzmann Equation
- Adaptive Space-Time Finite Element Methods for Non-autonomous Parabolic Problems with Distributional Sources
- On Convergence of Difference Schemes for Dirichlet IBVP for Two-Dimensional Quasilinear Parabolic Equations with Mixed Derivatives and Generalized Solutions
- Difference Schemes on Uniform Grids for an Initial-Boundary Value Problem for a Singularly Perturbed Parabolic Convection-Diffusion Equation
- A Finite Element Splitting Method for a Convection-Diffusion Problem
- Incomplete Iterative Implicit Schemes
- Explicit Runge–Kutta Methods Combined with Advanced Versions of the Richardson Extrapolation
- Regular Research Articles
- A General Superapproximation Result
- A First-Order Explicit-Implicit Splitting Method for a Convection-Diffusion Problem
- A Factorization of Least-Squares Projection Schemes for Ill-Posed Problems
- A New Mixed Functional-probabilistic Approach for Finite Element Accuracy
- Error Analysis of a Finite Difference Method on Graded Meshes for a Multiterm Time-Fractional Initial-Boundary Value Problem
- A Finite Element Method for Elliptic Dirichlet Boundary Control Problems
Artikel in diesem Heft
- Frontmatter
- Editorial
- Modern Problems of Numerical Analysis. On the Centenary of the Birth of Alexander Andreevich Samarskii
- Special Issue Articles
- Finite Difference Approximation of a Generalized Time-Fractional Telegraph Equation
- Weighted Estimates for Boundary Value Problems with Fractional Derivatives
- Lagrangian Mixed Finite Element Methods for Nonlinear Thin Shell Problems
- Reliable Computer Simulation Methods for Electrostatic Biomolecular Models Based on the Poisson–Boltzmann Equation
- Adaptive Space-Time Finite Element Methods for Non-autonomous Parabolic Problems with Distributional Sources
- On Convergence of Difference Schemes for Dirichlet IBVP for Two-Dimensional Quasilinear Parabolic Equations with Mixed Derivatives and Generalized Solutions
- Difference Schemes on Uniform Grids for an Initial-Boundary Value Problem for a Singularly Perturbed Parabolic Convection-Diffusion Equation
- A Finite Element Splitting Method for a Convection-Diffusion Problem
- Incomplete Iterative Implicit Schemes
- Explicit Runge–Kutta Methods Combined with Advanced Versions of the Richardson Extrapolation
- Regular Research Articles
- A General Superapproximation Result
- A First-Order Explicit-Implicit Splitting Method for a Convection-Diffusion Problem
- A Factorization of Least-Squares Projection Schemes for Ill-Posed Problems
- A New Mixed Functional-probabilistic Approach for Finite Element Accuracy
- Error Analysis of a Finite Difference Method on Graded Meshes for a Multiterm Time-Fractional Initial-Boundary Value Problem
- A Finite Element Method for Elliptic Dirichlet Boundary Control Problems
