# Guaranteed error bounds for finite element approximations of noncoercive elliptic problems and their applications

@article{Nakao2008GuaranteedEB, title={Guaranteed error bounds for finite element approximations of noncoercive elliptic problems and their applications}, author={Mitsuhiro T. Nakao and Kouji Hashimoto}, journal={Journal of Computational and Applied Mathematics}, year={2008}, volume={218}, pages={106-115} }

## 14 Citations

A posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations

- MathematicsMath. Comput.
- 2013

This paper presents constructive a posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations (PDEs) on a bounded domain. This type of…

Inverse norm estimation of perturbed Laplace operators and corresponding eigenvalue problems

- MathematicsComput. Math. Appl.
- 2022

Finite Element Approximation of Invariant Manifolds by the Parameterization Method

- Mathematics
- 2019

We combine the parameterization method for invariant manifolds with the finite element method for elliptic PDEs, to obtain a new computational framework for high order approximation of invariant…

An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces

- MathematicsJournal of Differential Equations
- 2019

Infinite-Dimensional Newton-Type Method

- MathematicsSpringer Series in Computational Mathematics
- 2019

This chapter presents two numerical verification methods which are based on some infinite-dimensional fixed-point theorems. The first approach is a technique using sequential iteration. Although this…

A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration

- MathematicsAppl. Math. Comput.
- 2016

Development of computer assisted analysis for complicated nonlinear phenomena

- Computer Science
- 2011

The present research aims, based on the existent products for stationary problems, at further development of new verification techniques, including evolutional equations, to establish the computer assisted proof as an important methodology of mathematical analysis in this century.

A new formulation for the numerical proof of the existence of solutions to elliptic problems

- MathematicsArXiv
- 2019

This paper represents the inverse operator ${\mathcal L}^{-1} as an infinite-dimensional operator matrix that can be decomposed into two parts, one finite dimensional and one infinite dimensional, enabling a more efficient verification procedure compared with existing methods for the solution of elliptic PDEs.

A numerical approach to the proof of existence of solutions for some generalized obstacle problems

- Mathematics, Computer ScienceAppl. Math. Comput.
- 2010

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