A numerical method for solving partial differential equations on highly irregular evolving grids

The application of the geometrical concept of 'natural neighbors' theory to the weighted residual method helps in solving partial differential equations on highly irregular evolving grids. This approach can effectively deal with problems involving large deformation and solid-fluid interactions on a deforming mesh. A two-dimensional example of a sinking elasto-plastic plate in a linear viscosity fluid is used to illustrate the updating of the mesh nodes and the connections between nodes during the calculation.