Dirichlet problem for Laplace–Beltrami equation on hypersurfaces—FEM approximation

Abstract

We consider Dirichlet boundary value problem for Laplace–Beltrami Equation On Hypersurface $S$, when the Laplace–Beltrami operator on the surface is described explicitly in terms of Günter’s differential operators. Using the calculus of Günter’s tangential differential operators on hypersurfaces we establish Finite Element Method for the considered boundary value problem and obtain approximate solution in explicit form.