. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Tiivistelmä (in Finnish) . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Fully discrete discontinuous Galerkin methods with variable meshes in time are developed for the fourth order Cahn-Hilliard equation arising from phase transition in materials science. The methods are formulated and analyzed in both two and three dimensions, and are proved to give optimal order error bounds. This coupled with the flexibility of the methods demonstrates that the proposed discont...

We develop new stabilized mixed finite element methods for Darcy flow. Stability and an a priori error estimate in the ‘‘stability norm’’ are established. A wide variety of convergent finite elements present themselves, unlike the classical Galerkin formulation which requires highly specialized elements. An interesting feature of the formulation is that there are no mesh-dependent parameters. N...

ה ןויעה םוי 35 חשיא לש " מ 0 1 רבוטקואב 013 2 , ןב תטיסרבינוא ןוירוג , ראב עבש , לארשי

We compare numerically the performance of a new continuous-discontinuous finite element method (CDFEM) for linear convection-diffusion equations with three well-known upwind finite element formulations, namely with the streamline upwind Petrov-Galerkin finite element method, the residualfree bubble method and the discontinuous Galerkin finite element method. The defining feature of the CDFEM is...

The project focused on the development, analysis, implementation, and application of efficient and high-order accurate methods formulti-scale and stochastic problems. Research focused on three topics: (1) High order weighted essentially non-oscillatory finite difference and finite volume schemes,discontinuous Galerkin finite elementmethod, and related methods, for solving comput...

Abstract. A C0-weak Galerkin (WG) method is introduced and analyzed for solving the biharmonic equation in 2D and 3D. A weak Laplacian is defined for C0 functions in the new weak formulation. This WG finite element formulation is symmetric, positive definite and parameter free. Optimal order error estimates are established in both a discrete H2 norm and the L2 norm, for the weak Galerkin finite...

A space-time Galerkin/least-squares finite element method was presented in [l] for numerical simulation of single-carrier hydrodynamic semiconductor device equations. The single-carrier hydrodynamic device equations were shown to resemble the ideal gas equations and Galerkin/least-squares finite element method, originally developed for computational fluid dynamics equations [16], was extended t...

We present spectral element (SE) and discontinuous Galerkin (DG) solutions of the Euler and compressible Navier– Stokes (NS) equations for stratified fluid flow which are of importance in nonhydrostatic mesoscale atmospheric modeling. We study three different forms of the governing equations using seven test cases. Three test cases involve flow over mountains which require the implementation of...