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- W2527415792 abstract "In this paper we introduce a discretisation of Discontinuous Galerkin (DG) type for solving 2-D second order elliptic PDEs on a regular rectangular grid, while the boundary value problem has a curved Dirichlet boundary. According to the same principles that underlie DG-methods, we adapt the discretisation in the cell in which the (embedded) Dirichlet boundary cannot follow the gridlines of the orthogonal grid.The DG-discretisation aims at a high order of accuracy. We discretize with tensor products of cubic polynomials. By construction, such a DG discretisation is fourth order consistent, both in the interior and at the boundaries. By experiments we show fourth order convergence in the presence of a curved Dirichlet boundary. Stability is proved for the one-dimensional Poisson equation with an embedded boundary condition.To illustrate the possibilities of our DG-discretisation, we solve a convection dominated boundary value problem on a regular rectangular grid with a circular embedded boundary condition [7]. We show how accurately the boundary layer with a complex structure can be captured by means of piece-wise cubic polynomials. The example shows that the embedded boundary treatment is effective." @default.
- W2527415792 created "2016-10-07" @default.
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- W2527415792 date "2003-01-01" @default.
- W2527415792 modified "2023-09-28" @default.
- W2527415792 title "On a two-dimensional discontinuous Galerkin discretisation with embedded Dirichlet boundary condition" @default.
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