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The scheme has a local stencil, is locally conservative, treats discontinuity rigorously and leads to a symmetric positive definite linear system.
She called a local stencil expert, who reconstructed the original design of a house and trees within an oval, a pattern dating to the 1920s.
The framework of this method consists of an adaptive local stencil refinement algorithm and 3-points central difference discretization.
We describe PPML, a local stencil variant of the popular PPM algorithm for solving the equations of compressible ideal magnetohydrodynamics.
The resulting numerical scheme, named CCLAD (Cell-Centered LAgrangian Diffusion), is characterized by a local stencil and cell-centered unknowns.
The method is based on a combination of the operator-splitting method, Godunov method, and piecewise-parabolic method on the local stencil.
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The method is of comparable quality to WENO schemes, but with optimally local stencils (performing updates in time by using information from only a single adjacent grid cell).
In addition, a simple, generalized procedure is developed to obtain the interpolation coefficients in a local reconstruction stencil explicitly from the geometric relationship.
For global RBFs, spectral spatial convergence is observed for smooth solutions on quasi-uniform nodes, while high-order accuracy is observed for the local RBF stencil and partition of unity approaches.
The three new methods are based on interpolation using 1) global RBFs, 2) local RBF stencils, and 3) RBF partition of unity.
The Poisson equation is solved to high-order via the smallest stencil local discontinuous Galerkin (LDG) approach.
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