Goal-Oriented A-Posteriori Error Estimation and Adaptivity for Fluid-Structure Interaction

Numerical simulation of fluid-structure interaction generally requires vast computational resources. Paradoxically, the computational work is dominated by the complexity of the subsystem that is of least practical interest, viz. the fluid. The resolution of each of the many small-scale features in the fluid is prohibitively expensive. However,...

An H1(Ph)-Coercive Discontinuous Galerkin Formulation for The Poisson Problem: 1-D Analysis

Coercivity of the bilinear form in a continuum variational problem is a fundamental property for finite-element discretizations: By the classical Lax–Milgram theorem, any conforming discretization of a coercive variational problem is stable; i.e., discrete approximations are well-posed and possess unique solutions, irrespective of the specifics...

Discontinuous Galerkin methods with solenoidal elements for the Stokes problem

The essential difficulty in the numerical solution of the incompressible Navier-Stokes (NS) equations is the coupling between the pressure and the velocity. The coupling enforces a constraint on the relation between the pressure and the velocity space. This constraint can be studied using a simplified form of the NS equations, viz. the Stokes...

Dual-based a-posteriori error estimation for fluid-structure interaction by the embedded-domain method

Numerical simulations of fluid-structure interaction typically require vast computational resources. Finite-element techniques employing goal-oriented hp-adaptation strategies could offer a substantial improvement in the efficiency of such simulations. These strategies rely on dual-based a-posteriori error estimates for quantities of interest....

Dual-based a-posteriori error estimation for fluid-structure interaction by the embedded-domain method

Numerical simulations of fluid-structure interaction typically require vast computational resources. Finite-element techniques employing goal-oriented hp-adaptation strategies could offer a substantial improvement in the efficiency of such simulations. These strategies rely on dual-based a-posteriori error estimates for quantities of interest....

Space/Time Multigrid for a Fluid-Structure-Interaction Problem

The basic iterative method for solving fluid-structure-interaction problems is a defect-correction process based on a partitioning of the underlying operator into a fluid part and a structural part. In the present work we establish for a prototypical model problem that this defect-correction process yields an excellent smoother for multigrid, on...

An H1(Ph)-Coercive Discontinuous Galerkin Formulation for the Poisson Problem: 1-D Analysis

Discontinuous Galerkin (DG) methods are finite element techniques for the solution of partial differential equations. They allow shape functions which are discontinuous across inter-element edges. In principle, DG methods are ideally suited for hp-adaptivity, as they handle nonconforming meshes and varying-in-space polynomial-degree...

An H1(Ph)-Coercive Discontinuous Galerkin Formulation for The Poisson Problem: 1-D Analysis

Discontinuous Galerkin (DG) methods are finite element techniques for the solution of partial differential equations. They allow shape functions which are discontinuous across inter-element edges. In principle, DG methods are ideally suited for hp-adaptivity, as they handle nonconforming meshes and varying-in-space polynomial-degree...