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If we discretize a parabolic pde to obtain the system of ODE's $\frac{\boldsymbol{B}}{\Delta t} \boldsymbol{u}_k = (\boldsymbol{K} + \frac{1}{\Delta t}) \boldsymbol{u}_{k-1} + \boldsymbol{f}_k$$\frac{\boldsymbol{B}}{\Delta t} \boldsymbol{u}_k = (\boldsymbol{K} + \frac{\boldsymbol{B}}{\Delta t}) \boldsymbol{u}_{k-1} + \boldsymbol{f}_k$ where $\boldsymbol{B}$ is the mass while $\boldsymbol{K}$ is the stiffness matrix, is there any condition on $\frac{\boldsymbol{B}}{\Delta t}$ such that this system is stable?

This system results from discretizing a parabolic PDE via forward Euler.

If we discretize a parabolic pde to obtain the system of ODE's $\frac{\boldsymbol{B}}{\Delta t} \boldsymbol{u}_k = (\boldsymbol{K} + \frac{1}{\Delta t}) \boldsymbol{u}_{k-1} + \boldsymbol{f}_k$ where $\boldsymbol{B}$ is the mass while $\boldsymbol{K}$ is the stiffness matrix, is there any condition on $\frac{\boldsymbol{B}}{\Delta t}$ such that this system is stable?

This system results from discretizing a parabolic PDE via forward Euler.

If we discretize a parabolic pde to obtain the system of ODE's $\frac{\boldsymbol{B}}{\Delta t} \boldsymbol{u}_k = (\boldsymbol{K} + \frac{\boldsymbol{B}}{\Delta t}) \boldsymbol{u}_{k-1} + \boldsymbol{f}_k$ where $\boldsymbol{B}$ is the mass while $\boldsymbol{K}$ is the stiffness matrix, is there any condition on $\frac{\boldsymbol{B}}{\Delta t}$ such that this system is stable?

This system results from discretizing a parabolic PDE via forward Euler.

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secondrate
secondrate
  • 161
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Stability condition for explicit time FEM for parabolic pdes

If we discretize a parabolic pde to obtain the system of ODE's $\frac{\boldsymbol{B}}{\Delta t} \boldsymbol{u}_k = (\boldsymbol{K} + \frac{1}{\Delta t}) \boldsymbol{u}_{k-1} + \boldsymbol{f}_k$ where $\boldsymbol{B}$ is the mass while $\boldsymbol{K}$ is the stiffness matrix, is there any condition on $\frac{\boldsymbol{B}}{\Delta t}$ such that this system is stable?

This system results from discretizing a parabolic PDE via forward Euler.