Abstract
In this paper, we consider numerical approximations of the volume-conserved phase-field elastic bending energy model for lipid vesicles where a nonlocal term is added to the model such that the total volume can be conserved precisely. We further develop two linear and unconditionally energy stable schemes by combining the recently developed IEQ and SAV approaches with the stabilization technique, where several extra stabilization terms are added to enhance the stability and keep the required accuracy while using large time steps. Through the comparisons with some other type numerical schemes for simulating numerous benchmarking numerical examples in 2D and 3D, we demonstrate the robustness of the new nonlocal volume-conserved model, as well as the stability and the accuracy of the developed schemes, numerically.
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