Summary: A p-th Degree Immersed Finite Element for Boundary Value
Problems with Discontinuous Coefficients
Slimane Adjerid and Tao Lin
Department of Mathematics
Virginia Polytechnic Institute and State University
Blacksburg, VA 24061-0123
In this manuscript we present a p-th degree immersed finite element method for solving boundary
value problems with discontinuous coefficients. In this method, interface jump conditions are employed in
the finite element basis functions, and the mesh does not have to be aligned with coefficient discontinuity.
We show that under h refinement the immersed finite element solution converges to the true solution at
the optimal O(hp+1
) and O(hp
) rates in the L2
norms, respectively. Furthermore, we show that
the immersed finite element solution converges exponentially fast under p refinement and hp refinement.
Numerical examples are provided to illustrate features of this immersed finite element method.
Keywords: Immersed finite elements, higher order methods, discontinuous coefficients