A second order multipoint flux mixed finite element method on hybrid meshes

Bogdan Radu M.Sc.

Oct. 19, 2021, 3:30 p.m. S3 048

We consider the numerical approximation of subsurface flow problems by a mixed finite element method. Following ideas of Wheeler and Yotov, we utilize a mass-lumping strategy that allows us to circumvent the saddle point structure of the underlying variational problem by local elimination of the flux variables leading to a Poisson-type problem for the pressure only. We present a convergence analysis, which allows us to obtain order optimal second order approximations. The theoretical results will be illustrated by numerical tests which demonstrate the efficiency of the method.