Speaker
Description
Nonconforming surface finite elements have recently been developed to discretize 3D vector-valued compressible flow problems arising in climate modeling. In this talk, we present an error analysis of this approach for a vector-valued Laplace problem, a key operator in fluid equations on surfaces. The problem is discretized via edge-integration on local flat triangles using the nonconforming linear Crouzeix–Raviart element, which is continuous at edge midpoints in each vector component. We first introduce the vector-valued Laplace problem on the surface and its Crouzeix–Raviart discretization. We then present interpolation estimates and derive optimal error bounds in the H^1- and L^2-norms. Finally, we show numerical experiments validating the theoretical convergence rates.