## Interior estimates for Ritz-Galerkin methods

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- by Joachim A. Nitsche and Alfred H. Schatz PDF
- Math. Comp.
**28**(1974), 937-958 Request permission

## Abstract:

Interior a priori error estimates in Sobolev norms are derived from interior Ritz-Galerkin equations which are common to a class of methods used in approximating solutions of second order elliptic boundary value problems. The estimates are valid for a large class of piecewise polynomial subspaces used in practice, which are defined on both uniform and nonuniform meshes. It is shown that the error in an interior domain $\Omega$ can be estimated with the best order of accuracy that is possible locally for the subspaces used plus the error in a weaker norm over a slightly larger domain which measures the effects from outside of the domain $\Omega$. Additional results are given in the case when the subspaces are defined on a uniform mesh. Applications to specific boundary value problems are given.## References

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## Additional Information

- © Copyright 1974 American Mathematical Society
- Journal: Math. Comp.
**28**(1974), 937-958 - MSC: Primary 65N30; Secondary 35JXX
- DOI: https://doi.org/10.1090/S0025-5718-1974-0373325-9
- MathSciNet review: 0373325