Title: A new theory for movement of surface meshes
Abstract: We will propose an approach for mesh adaptation on surfaces that, to our best knowledge, is the only surface moving mesh method that can be directly applied to a general surface. We will formulate a surface functional based on the equidistribution and alignment conditions and employ a new surface MMPDE method to find its minimizer. We will then discuss and prove various theoretical properties, including that the mesh stays nonsingular for all time if it is so initially. Finally, we will present various numerical results in two and three-dimensions.