An interface-fitted adaptive mesh method for elliptic problems and its application in free interface problems with surface tension
The paper describes the interface-fitted mesh generation technique and the piecewise linear finite element method for elliptic problems with a general class of jump conditions across the interface. Almost optimal a priori estimates in both \(H^1\) and \(L^2\) norms are proved in this case for both Dirichlet and Neumann problems. Especially, almost the second-order convergence in the region away from the interface in the \(L^2\) norm is obtained. Besides elliptic problems, the method is applied to the Stokes flow and to a tumour growth problem, where Darcy's equations are solved.
scientific article; zbMATH DE number 6674202
scientific article