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This paper deals with a general framework for a posteriori error estimates in boundary element methods which is specified for three examples, namely Symm's integral equation, an integral equation with a hypersingular operator, and a boundary integral equation for a transmission problem. Based on these estimates, an analog of Eriksson and Johnson's adaptive… (More)

- Benqi Guo, Ernst P. Stephan
- Numerische Mathematik
- 1998

- Carsten Carstensen, Matthias Maischak, Ernst P. Stephan
- Numerische Mathematik
- 2001

- Carsten Carstensen, Matthias Maischak, Dirk Praetorius, Ernst P. Stephan
- Numerische Mathematik
- 2004

- Norbert Heuer, Ernst P. Stephan, Thanh Tran
- Math. Comput.
- 1998

We study a multilevel additive Schwarz method for the h-p version of the Galerkin boundary element method with geometrically graded meshes. Both hypersingular and weakly singular integral equations of the first kind are considered. As it is well known the h-p version with geometric meshes converges exponentially fast in the energy norm. However, the… (More)

We consider weakly singular integral equations of the rst kind on screens in IR 3. To obtain approximate solutions we use the hand p-versions of the Galerkin Boundary Element Method. We introduce two-level additive Schwarz operators with bounded condition numbers. Based on these operators we derive an a posteriori error estimate for the diierence between… (More)

- Hinrich Holm, Matthias Maischak, Ernst P. Stephan
- Computing
- 1996

We study the boundary element method for weakly singular and hypersingular integral equations of the first kind on screens resulting from the Dirichlet and Neumann problems for the Helmholtz equation. It is shown that the hp-version with geometrical refined meshes converges exponentially fast in both cases. We underline our theoretical results by numerical… (More)

- Patrick Mund, Ernst P. Stephan, J. Weiße
- Computing
- 1998

We consider weakly singular integral equations of the first kind on open surface pieces Γ in ℝ3. To obtain approximate solutions we use theh-version Galerkin boundary element method. Furthermore we introduce two-level additive Schwarz operators for non-overlapping domain decompositions of Γ and we estimate the conditions numbers of these operators with… (More)

- Norbert Heuer, Ernst P. Stephan
- SIAM J. Scientific Computing
- 1998

In this work we introduce a new a posteriori error estimate of hierarchical type for the advection-diffusion-reaction equation. We prove the equivalence between the energy norm of the error and our error estimate using an auxiliary linear problem for the residual and an easy way to prove inf–sup condition.