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What is it called when we interpolate a point INTO a grid…

Consider a uniform 2D grid, where each $(x,y)$ value on this grid has a corresponding value. So, if I want to find the value, $v$ (unknown) of a point that exists at some arbitrary co-ordinate $(x,y)$ ...
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Numerical Overflow in Dirichlet Boundary Value Problem On High Dimensional State

I am using multigrid methods to solve a quasilinear parabolic pde with Dirichlet boundaries. The problem is too long to reproduce here, but my question is more practical than theoretical: The state ...
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Numbering Elements of Quadrilateral Mesh

I am having a Regular Structured Quadrilateral Mesh of size = $A \times B \times C$. The ID of the grids starts from $s$, that means $(0,0,0)$ will be $s$ and $(0,0,1)$ will be $s+1$. Now, I am ...
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Calculating h-ellipticity

How do we calculate h-ellipticity $E_{h}$ of standard five point discrete Laplacian of two dimensional partial differential equation?
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Isoparametric mapping

I have a some points and I want to map it to another shape (shown in picture). Can anybody explain me how to do it step by step and how many known points coordinate from the mapped shape do I need to ...
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Multigrid Interpolation and Restriction operators

I have a question about the restriction and the interpolation operators of a Multigrid algorithm. Let those be given: The full weighting restriction stencil (in 2D): $\frac{1}{16} \left[ ...
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Addressing/traversing an infinite 2D grid using a Z-line?

I'm looking for a method to map an infinite 2D grid using a line, so that I would have just one integer from which I would compute the X and Y. I know something like that exists, but can't recall the ...
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Multigrid tutorial/book

I was reading Press et. al., "Numerical Recipes" book, which contain section about multigrid method for numerically solving boundary value problems. However, the chapter is quite brief and I would ...