Bernstein-Bézier Galerkin-Characteristics Finite Element Method for Convection-Diffusion Problems

Abstract A class of Bernstein-Bézier basis based high-order finite element methods is developed for the Galerkin-characteristics solution convection-diffusion problems. The formulation derived using a semi-Lagrangian discretization total derivative in considered spatial performed method on unstructured meshes. Lagrangian interpretation this approach greatly reduces time truncation errors Eulerian methods. To achieve accuracy solver, requires interpolating procedures. In present work, step carried out functions to evaluate at departure points. Triangular patches are constructed simple and inherent manner over elements along characteristics. An efficient preconditioned conjugate gradient solver used linear systems algebraic equations. Several numerical examples including advection-diffusion equations with known analytical solutions viscous Burgers problem illustrate accuracy, robustness performance proposed approach. computed results support our expectations stable highly accurate