We present a finite element approximation of motion by minus the Laplacian of curvature and related flows. The proposed scheme covers both the closed curve case, and the case of curves that are connected via triple junctions. On introducing a parametric finite element approximation, we prove stability bounds and compare our scheme with existing approaches. It turns out that the new scheme has v...

Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyse fully discrete numerical method this geometric evolution equation. The uses piecewise linear finite elements in space and backward Euler approximation time. We establish existence uniqueness solution, as well an unconditional stability property. Some computations confirm the theoretical results demon...

Based on H-Galerkin mixed finite element method with nonconforming quasi-Wilson element, a numerical approximate scheme is established for pseudo-hyperbolic equations under arbitrary quadrilateral meshes. The corresponding optimal order error estimate is derived by the interpolation technique instead of the generalized elliptic projection which is necessary for classical error estimates of fini...