Second-order PFEMs for surface diffusion achieve exact area/volume preservation via Simpson-Boole geometric identities on quadratic interpolants without auxiliary multipliers.
Barrett, Harald Garcke, and Robert N¨ urnberg
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Develops an evolving finite element method for parabolic PDEs with evolving interfaces, derives a suitable weak formulation, proves optimal error bounds for isoparametric elements of arbitrary order, and verifies convergence numerically.
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Second-Order Area/Volume-Preserving PFEMs for Surface Diffusion via Simpson--Boole Geometric Identities
Second-order PFEMs for surface diffusion achieve exact area/volume preservation via Simpson-Boole geometric identities on quadratic interpolants without auxiliary multipliers.
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Evolving finite elements for advection diffusion with an evolving interface
Develops an evolving finite element method for parabolic PDEs with evolving interfaces, derives a suitable weak formulation, proves optimal error bounds for isoparametric elements of arbitrary order, and verifies convergence numerically.