Development of a method for solving elliptic differential equations based on a nonlinear compact-polynomial scheme

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Navier-Stokes equations for incompressible viscous fluids (76D05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Cites Work

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Quasi-rational function solutions of an elliptic equation and its application to solve some nonlinear evolution equations
Fourth-order accurate bicompact schemes for hyperbolic equations
A new convergence proof of the Adomian decomposition method for a mixed hyperbolic elliptic system of conservation laws
Convergence acceleration of the rational Runge-Kutta scheme for the Euler and Navier-Stokes equations
Monotone finite volume schemes for diffusion equations on polygonal meshes
High-order mimetic finite difference method for diffusion problems on polygonal meshes
A family of monotone methods for the numerical solution of three-dimensional diffusion problems on unstructured tetrahedral meshes
A monotone finite volume method for advection-diffusion equations on unstructured polygonal meshes
Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes
Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy
Dimensional scaling and numerical similarity in hyperbolic method for diffusion
Construction of monotone difference schemes for systems of hyperbolic equations
A fully discrete two-grid finite element method for nonlinear hyperbolic integro-differential equation
A first-order system approach for diffusion equation. I: Second-order residual-distribution schemes
Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes
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Monotone compact running schemes for systems of hyperbolic equations
A compact multipoint flux approximation method with improved robustness
A monotone nonlinear finite volume method for advection–diffusion equations on unstructured polyhedral meshes in 3D
A monotone nonlinear finite volume method for diffusion equations on conformal polyhedral meshes
Two splitting schemes for nonstationary convection-diffusion problems on tetrahedral meshes
The construction of difference schemes of increased order of accuracy for equations of hyperbolic type
Mixed and Hybrid Finite Element Methods
Construction of schemes of prescribed order of accuracy with linear combinations of operators
Dynamics of two vortex rings in a Bose-Einstein condensate

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