Semidiscrete finite element methods for linear and semilinear parabolic problems with smooth interfaces: Some new optimal error estimates

摘要

Semidiscrete finite element approximations of the linear and semilinear parabolic interface problems are studied in the article. The convergence of the finite element solutions to the exact solutions are analyzed for fitted finite element method with straight interface triangles. Under practical regularity assumptions of the true solution it seems difficult to achieve optimal order convergence with straight interface triangles. In this exposition optimal error estimates in the L ~2(L ~2) and L ~2(H ~1) norms are established for linear semidiscrete scheme. Then an extension to the semilinear problem is also considered and related optimal error estimates are achieved. The interfaces are assumed to be smooth for our purpose.