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Short Answer: There is no general result that would hold for all implicit schemes. The reason is that how your method behaves with respect to numerical diffusion depends on the specific combination of numerical time stepping scheme and spatial finite difference. However, note that if your discretisation is consistent with your PDE and your PDE does not have ...


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This is one of those scenarios where assessing the convergence order of your scheme is difficult, because, as you explained, your time-step is "linked" to your spatial discretization. What you could do is manufacture an analytical problem without any spatial error. For example, in finite elements, if you are using P2 polynomials, a second order ...


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Yes. That's all there is to the stability condition. Taking the material properties - shear modulus ($\mu$), bulk modulus ($\kappa$) and density ($\rho$) - into account, the global critical time step is evaluated as the minimum of the critical time step for each element ($\Delta t^e$) $\Delta t^e = CFL * h^e / c_{\kappa}$ where CFL is the Courant-Friedrichs-...


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