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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

1 vote

Analytical testcase for 2D/3D anisotropic Diffusion (Heat Kernel)

Thanks to @Andrew I dug out the following solution: $$ u(\vec{x},\vec{\mu},t) = \frac{1}{(4\pi~ t)^{d/2}~\sqrt{|\mathbf{D}|}} \exp \large(\frac{-(\vec{x}-\vec{\mu})^{T} \mathbf{D}^{-1}(\vec{x}-\vec{\ …
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Analytical testcase for 2D/3D anisotropic Diffusion (Heat Kernel)

I want to verify and compare different Discretizations of the anisotropic diffusion equation in 2D / 3D image of my testsetting. I want to verify and compare different Discretizations of the anisotro …
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