Mixed finite element methods for geometric modeling using general fourth order geometric flows

A variational formulation of a general form fourth order geometric partial differential equation is derived, and based on which three versions of the mixed finite element method are developed. Several surface modeling problems, including surface denoising, surface blending, hole filling and surface mesh refinement with the G1 continuity, are taken into account. The used geometric partial differential equation is universal, containing several well-known geometric partial differential equations as its special cases. The proposed method is general which can be used to construct surfaces for geometric design as well as simulate the behaviors of various geometric partial differential equations. Experimental results show that the method is efficient and gives very desirable results.