| Abstract: |
| The finite element approximation of surface evolution under external velocity field is studied. A tangential motion is designed, by using harmonic map heat flow from a reference surface onto the evolving surface, to improve the mesh quality of the numerically computed surface. The convergence of evolving finite element approximations to the surface evolution driven by a specified vector field with the proposed tangential motion is proved for finite elements of degree $k\geq 3$. Numerical examples are provided to demonstrate the convergence of the algorithm and its effectiveness for improving the mesh quality of the numerically computed evolving surface. |
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