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High-order finite-difference ghost-point methods for elliptic problems in domains with curved boundaries
High-order finite-difference ghost-point methods for elliptic problems in domains with curved boundaries
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High-order finite-difference ghost-point methods for elliptic problems in domains with curved boundaries
High-order finite-difference ghost-point methods for elliptic problems in domains with curved boundaries

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High-order finite-difference ghost-point methods for elliptic problems in domains with curved boundaries
High-order finite-difference ghost-point methods for elliptic problems in domains with curved boundaries
Journal Article

High-order finite-difference ghost-point methods for elliptic problems in domains with curved boundaries

2024
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Overview
In this article, a fourth-order finite-difference ghost-point method for the Poisson equation on regular Cartesian mesh is presented. The method can be considered the high-order extension of the second-order ghost method introduced earlier by the authors. Three different discretizations are considered, which differ in the stencil that discretizes the Laplacian and the source term. It is shown that only two of them provide a stable method. The accuracy of such stable methods is numerically verified on several test problems.

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