UN CO RR EC TE D PR O O F 1 A Hybrid Discontinuous Galerkin Method 2 for Darcy - Stokes Problems 3

UN CO RR EC TE D PR O O F 1 BDDC for Higher - Order Discontinuous Galerkin 2 Discretizations 3

A Balancing Domain Decomposition by Constraints (BDDC) method is presented 13 for the solution of a discontinuous Galerkin (DG) discretization of a second-order 14 elliptic problem in two dimensions. BDDC was originally introduced in [8] for the 15 solution of continuous finite element discretizations. Mandel and Dohrmann [13] 16 later proved a condition number bound of κ ≤ C(1 + log(H/h))2 for...

UN CO RR EC TE D PR O O F 1 Penalty Robin - Robin Domain Decomposition Schemes 2 for Contact Problems of Nonlinear Elastic Bodies 3

UN CO RR EC TE D PR O O F 1 Mesh Regularization in Bank - Holst Parallel 2 hp - Adaptive Meshing 3 Randolph

UN CO RR EC TE D PR O O F 1 Domain Decomposition Methods for Auxiliary Linear 2 Problems of an Elliptic Variational Inequality 3

Elliptic variational inequalities with multiple bodies are considered. It is assumed 7 that an active set method is used to handle the nonlinearity of the inequality constraint, which 8 results in auxiliary linear problems. We describe two domain decomposition methods for solv9 ing such linear problems, namely, the FETI-FETI (finite element tearing and interconnecting) 10 and hybrid methods, wh...

A Hybrid Discontinuous Galerkin Method for Darcy-Stokes Problems

We propose and analyze a hybrid discontinuous Galerkin method for the solution of incompressible flow problems, which allows to deal with pure Stokes, pure Darcy, and coupled Darcy-Stokes flow in a unified manner. The flexibility of the method is demonstrated in numerical examples.