On the analysis and numerics of united and segregated boundary-domain integral equation systems in 2D. (English) Zbl 1524.65904
Summary: The boundary domain integral equation (BDIE) method provides an alternative formulation to a boundary value problem (BVP) with variable coefficient in terms of integral operators defined on the boundary and the domain. In this paper, we apply two variants of the boundary domain integral equation, the united approach and the segregated approach, to the Dirichlet BVP for the steady diffusion equation with variable coefficient in two dimensions. Details on the derivation of such systems as well as equivalence and well-posedness results are provided. Moreover, we present the discretisation of the two integral equation systems and a comparison of the numerical behaviour of the approximated solutions obtained with the segregated approach and the united approach.
MSC:
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 35J57 | Boundary value problems for second-order elliptic systems |
| 45P05 | Integral operators |
| 65R20 | Numerical methods for integral equations |
Keywords:
variable coefficient; parametrix; Dirichlet boundary value problem; united boundary-domain integral equations; segregated united boundary-domain integral equations; single layer potentialReferences:
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