Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element

@article{Yamamoto1995NumericalVF,
  title={Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element},
  author={Nobito Yamamoto and Mitsuhiro T. Nakao},
  journal={Journal of Computational and Applied Mathematics},
  year={1995},
  volume={60},
  pages={271-279}
}
  • N. YamamotoM. Nakao
  • Published 20 June 1995
  • Mathematics
  • Journal of Computational and Applied Mathematics

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References

SHOWING 1-10 OF 12 REFERENCES

Solving Nonlinear Elliptic Problems with Result Verification Using an H -1 Type Residual Iteration

Solving Nonlinear Elliptic Problems with Result Verification Using an H -1 Type Residual Iteration. In this paper, we consider a numerical technique to verify the solutions with guaranteed error

Numerical verifications of solutions for nonlinear elliptic equations

A numerical technique which enables us to verify the existence of weak solutions for nonlinear elliptic boundary value problems is proposed. It is based on the infinite dimensional fixed point

Numerical verifications of solutions for elliptic equations with strong nonlinearity

Numerical methods for automatic proof of the existence and the local uniqueness of weak solutions of elliptic boundary value problems with strongly nonlinear terms are proposed. They are based on the

A numerical approach to the proof of existence of solutions for elliptic problems II

This paper is a continuation of the preceding study ([2]) in which we described an automatic proof by computer, utilizing Schauder’s fixed point theorem, of the existence of weak solutions for

Numerical verifications of solutions for elliptic equations in nonconvex polygonal domains

SummaryIn this paper, methods for numerical verifications of solutions for elliptic equations in nonconvex polygonal domains are studied. In order to verify solutions using computer, it is necessary