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Full-Text Articles in Physical Sciences and Mathematics
Numerical Methods For Non-Divergence Form Second Order Linear Elliptic Partial Differential Equations And Discontinuous Ritz Methods For Problems From The Calculus Of Variations, Stefan Raymond Schnake
Numerical Methods For Non-Divergence Form Second Order Linear Elliptic Partial Differential Equations And Discontinuous Ritz Methods For Problems From The Calculus Of Variations, Stefan Raymond Schnake
Doctoral Dissertations
This dissertation consists of three integral parts. Part one studies discontinuous Galerkin approximations of a class of non-divergence form second order linear elliptic PDEs whose coefficients are only continuous. An interior penalty discontinuous Galerkin (IP-DG) method is developed for this class of PDEs. A complete analysis of the proposed IP-DG method is carried out, which includes proving the stability and error estimate in a discrete W2;p-norm [W^2,p-norm]. Part one also studies the convergence of the vanishing moment method for this class of PDEs. The vanishing moment method refers to a PDE technique for approximating these PDEs by a …
High Order Finite Elements For Lagrangian Computational Fluid Dynamics, Truman Everett Ellis
High Order Finite Elements For Lagrangian Computational Fluid Dynamics, Truman Everett Ellis
Master's Theses
A general finite element method is presented to solve the Euler equations in a Lagrangian reference frame. This FEM framework allows for separate arbitrarily high order representation of kinematic and thermodynamic variables. An accompanying hydrodynamics code written in Matlab is presented as a test-bed to experiment with various basis function choices. A wide range of basis function pairs are postulated and a few choices are developed further, including the bi-quadratic Q2-Q1d and Q2-Q2d elements. These are compared with a corresponding pair of low order bi-linear elements, traditional Q1-Q0 and sub-zonal pressure Q1-Q1d. Several test problems are considered including static convergence …