Explicit Constants in Poincaré-Type Inequalities for Simplicial Domains and Application to A Posteriori Estimates
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Svetlana Matculevich
und
Sergey Repin
Abstract
The paper is concerned with sharp estimates of constants in the classical Poincaré inequalities and Poincaré-type inequalities for functions with zero mean values in a simplicial domain or on a part of the boundary. These estimates are important for quantitative analysis of problems generated by differential equations where numerical approximations are typically constructed with the help of simplicial meshes. We suggest easily computable relations that provide sharp bounds of the respective constants and compare these results with analytical estimates (if such estimates are known). In the last section, we discuss possible applications and derive a computable majorant of the difference between the exact solution of a boundary value problem and an arbitrary finite dimensional approximation defined on a simplicial mesh.
Funding source: Suomalainen Tiedeakatemia Foundation
Funding source: RFBR
Award Identifier / Grant number: 14-01-00162/15
© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Vertex-Based Compatible Discrete Operator Schemes on Polyhedral Meshes for Advection-Diffusion Equations
- Reliable Averaging for the Primal Variable in the Courant FEM and Hierarchical Error Estimators on Red-Refined Meshes
- Monotone Finite Difference Schemes for Quasilinear Parabolic Problems with Mixed Boundary Conditions
- The Laguerre Collocation Method for Third Kind Integral Equations on Unbounded Domains
- Projection Methods for Ill-Posed Problems Revisited
- Explicit Constants in Poincaré-Type Inequalities for Simplicial Domains and Application to A Posteriori Estimates
- Regularization by Aggregation of Global and Local Data on the Sphere
- A Note on Lower Bounds of Eigenvalues of Fourth Order Elliptic Operators on Local Quasi-Uniform Grids
- Numerical Analysis and Computation of a Type of IMEX Method for the Time-Dependent Natural Convection Problem
- The Valuation of Carbon Bonds Linked with Carbon Price
Artikel in diesem Heft
- Frontmatter
- Vertex-Based Compatible Discrete Operator Schemes on Polyhedral Meshes for Advection-Diffusion Equations
- Reliable Averaging for the Primal Variable in the Courant FEM and Hierarchical Error Estimators on Red-Refined Meshes
- Monotone Finite Difference Schemes for Quasilinear Parabolic Problems with Mixed Boundary Conditions
- The Laguerre Collocation Method for Third Kind Integral Equations on Unbounded Domains
- Projection Methods for Ill-Posed Problems Revisited
- Explicit Constants in Poincaré-Type Inequalities for Simplicial Domains and Application to A Posteriori Estimates
- Regularization by Aggregation of Global and Local Data on the Sphere
- A Note on Lower Bounds of Eigenvalues of Fourth Order Elliptic Operators on Local Quasi-Uniform Grids
- Numerical Analysis and Computation of a Type of IMEX Method for the Time-Dependent Natural Convection Problem
- The Valuation of Carbon Bonds Linked with Carbon Price
