On the order of pointwise convergence of some boundary element methods. I: Operators of negative and zero order. (English) Zbl 0579.65147

Rannacher, R.; Wendland, W. L.

RAIRO, Modélisation Math. Anal. Numér. 19, 65-87 (1985).

The approximate solution of boundary integral equations and strongly elliptic pseudodifferential equations by the finite element Galerkin method are examined. For operators of order \(2\alpha\leq 0\) it is shown that the discrete solutions and for the case of some first kind integral equations also the traces of the corresponding potentials converge uniformly with almost the same optimal order as is known for their convergence in the mean square sense. The proof is based on error estimates for discrete Green functions which are derived by using weighted Sobolev norms and Garding’s inequality.

Reviewer: N.F.F.Ebecken

MSC:

65R20	Numerical methods for integral equations
65N35	Spectral, collocation and related methods for boundary value problems involving PDEs
45K05	Integro-partial differential equations
35S15	Boundary value problems for PDEs with pseudodifferential operators

Keywords:

boundary integral equations; strongly elliptic pseudodifferential equations; finite element Galerkin method; convergence; discrete Green functions; Garding’s inequality

References:

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