A direct finite-difference scheme for solving PDEs over general two-dimensional regions

Cortés-Medina, Adán; Chavez-Gonzalez, A. F.; Tinoco-Ruiz, José Gerardo

doi:10.1016/s0168-9274(01)00076-9

Cited by 2 publications

(1 citation statement)

References 3 publications

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“…GFDM has been widely applied for solving a collection of problems. Among several research works, we can mention the following: Cortés-Medina et al [14] used GFDM for solving the Poisson equation over general and very irregular twodimensional regions. Benito et al [15] implemented GFDM with explicit methods for solving parabolic and hyperbolic equations, using irregular grids of points, this shows that GFDM can also be applied as a meshless method.…”

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confidence: 99%

Numerical solution of density-driven groundwater flows using a generalized finite difference method defined by an unweighted least-squares problem

Román-Gutiérrez

Chávez-Negrete

Domínguez-Mota

et al. 2022

Front. Appl. Math. Stat.

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Density-driven groundwater flows are described by nonlinear coupled differential equations. Due to its importance in engineering and earth science, several linearizations and semi-linearization schemes for approximating their solution have been proposed. Among the more efficient are the combinations of Newtonian iterations for the spatially discretized system obtained by either scalar homotopy methods, fictitious time methods, or meshless generalized finite difference method, with several implicit methods for the time integration. However, when these methods are used, some parameters need to be determined, in some cases, even manually. To overcome this problem, this paper presents a novel generalized finite differences scheme combined with an adaptive step-size method, which can be applied for solving the governing equations of interest on non-rectangular structured and unstructured grids. The proposed method is tested on the Henry and the Elder problems to verify the accuracy and the stability of the proposed numerical scheme.

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Section: Figurementioning

confidence: 99%

Numerical solution of density-driven groundwater flows using a generalized finite difference method defined by an unweighted least-squares problem

Román-Gutiérrez

Chávez-Negrete

Domínguez-Mota

et al. 2022

Front. Appl. Math. Stat.

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An heuristic finite difference scheme on irregular plane regions

Domínguez-Mota¹,

Fernandez-Valdez²,

Ruiz-Diaz³

et al. 2014

ams

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In this paper, we present an heuristic finite difference scheme for the second-order linear operator, which is derived from an unconstrained least squares problem defined by the consistency condition on the residuals of order one, two and three in the Taylor expansion of the local truncation error. It is based on a non-iterative calculation of the difference coefficients and can be used to solve efficiently Poisson-like equations on non-rectangular domains which are approximated by structured convex grids.

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A direct finite-difference scheme for solving PDEs over general two-dimensional regions

Cited by 2 publications

References 3 publications

Numerical solution of density-driven groundwater flows using a generalized finite difference method defined by an unweighted least-squares problem

Numerical solution of density-driven groundwater flows using a generalized finite difference method defined by an unweighted least-squares problem

An heuristic finite difference scheme on irregular plane regions

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