A Divergence-Free Relaxation Scheme in an H^1-Finite Element Space: Numerical Results and Theory

Travis Austin

Department of Applied Mathematics Campus Box 526, CU Boulder, CO 80309-0526


An effective multilevel solver for (I - grad div) must account for the presence of divergence-free error components. As a result, the Raviart-Thomas (RT) finite element spaces, with locally computable divergence-free subspaces, are often used in the discretization of (I - grad div). The presence of an epsilon-sized Laplacian term, leading to (I - eps*Laplacian - grad div), results in poor approximation properties for the discontinuous RT finite element spaces. With a new continuous, RT-like finite element space, we can define a multilevel solution algorithm which achieves optimal convergence factors. In this talk, we will present numerical results validating our claim and introduce theory to firmly establish the algorithms effectiveness.