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We apply high-order mixed finite element discretization techniques and theirassociated preconditioned iterative solvers to the Variable Eddington Factor(VEF) equations in two spatial dimensions. The mixed finite element VEFdiscretizations are coupled to a high-order Discontinuous Galerkin (DG)discretization of the Discrete Ordinates transport equation to form effectivelinear transport algorithms that are compatible with high-order (curved)meshes. This combination of VEF and transport discretizations is motivated bythe use of high-order mixed finite element methods in hydrodynamicscalculations at the Lawrence Livermore National Laboratory. Due to themathematical structure of the VEF equations, the standard Raviart Thomas (RT)mixed finite elements cannot be used to approximate the vector variable in theVEF equations. Instead, we investigate three alternatives based on the use ofcontinuous finite elements for each vector component, a non-conforming RTapproach where DG-like techniques are used, and a hybridized RT method. Wepresent numerical results that demonstrate high-order accuracy, compatibilitywith curved meshes, and robust and efficient convergence in iteratively solvingthe coupled transport-VEF system and in the preconditioned linear solvers usedto invert the discretized VEF equations.

High-Order Mixed Finite Element Variable Eddington Factor Methods