Questions tagged [spectral-method]

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4
votes
4answers
498 views

Role of weight function in Galerkin methods

I have difficulties in understanding the role of the weight function $w(x)$ that occurs in the solution of PDEs via the Galerkin approach. Consider a linear differential equation of the form $$ \...
3
votes
1answer
2k views

How do I form the Chebyshev differentiation matrix in MATLAB?

I have some code that does exactly this, but I do not like to use things I do not understand. Here is the code ...
7
votes
2answers
323 views

Spectral Methods in time

I was reading up on Spectral Methods for PDEs. In all the descriptions I read, while the position component is approximated via a Fourier series or other methods, the time component is still ...
4
votes
2answers
418 views

Interpolation with the roots of orthogonal polynomials & Spectral expansion

I'm a bit confused about the relationships between these two approximation methods mentioned in the title. Does this kind of interpolation also belongs to the field of spectral methods? Are the ...
3
votes
3answers
924 views

Solving Stokes flow with walls using Oseen tensor

Introduction I've developed a code to solve for generalised, incompressible 2D Stokes flow $\eta \nabla^2 \mathbf{v} - \nabla p + \mathbf{S} = 0$ $\nabla . \mathbf{v} = 0$ where $\mathbf{S}$ can ...