Goal-Oriented Error Estimation and Adaptivity for Free-Boundary Problems: The Shape-Linearization Approach

We develop duality-based a posteriori error estimates for functional outputs of solutions of free-boundary problems via shape-linearization principles. To derive an appropriate dual (linearized adjoint) problem, we linearize the domain dependence of the very weak form and goal functional of interest using techniques from shape calculus. We show...

Goal-Oriented Error Estimation and Adaptivity for Free-Boundary Problems: The Domain-Map Linearization Approach

In free-boundary problems, the accuracy of a goal quantity of interest depends on both the accuracy of the approximate solution and the accuracy of the domain approximation. We develop duality-based a posteriori error estimates for functional outputs of solutions of free-boundary problems that include both sources of error. The derivation of an...

Added Mass Effects of Compressible and Incompressible Flows in Fluid-Structure Interaction

The subiteration method which forms the basic iterative procedure for solving fluid structure-interaction problems is based on a partitioning of the fluid-structure system into a fluidic part and a structural part. In fluid-structure interaction, on short time scales the fluid appears as an added mass to the structural operator, and the...

A Space-Time Finite Element Approach to the Numerical Simulation of Vascular Fluid-Solid Interaction

Numerical studies of cardiovascular diseases like arteriosclerosis have gained increasing attention the last decade. The modeling of blood, blood vessel and their coupling, shows to be a challenging problem. In this thesis a two-dimensional model has been constructed and its behaviour has been investigated. We model the blood vessel by a linear...

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....

Validation of the interface-GMRES(R) solution method for fluid-structure interactions

The numerical solution of fluid-structure interactions with the customary subiteration method incurs numerous deficiencies. We validate a recently proposed solution method based on the conjugation of subiteration with a Newton-Krylov method, and demonstrate its superiority and beneficial characteristics.

Multiscale Methods in Computational Fluid and Solid Mechanics

The basic idea of multiscale methods, namely the decomposition of a problem into a coarse scale and a fine scale, has in an intuitive manner been used in engineering for many decades, if not for centuries. Also in computational science, large-scale problems have been solved, and local data, for instance displacements, forces or velocities, have...

Validation of the interface-GMRES(R) solution method for fluid-structure interactions

The numerical solution of fluid-structure interactions with the customary subiteration method incurs numerous deficiencies. We validate a recently proposed solution method based on the conjugation of subiteration with a Newton-Krylov method, and demonstrate its superiority and beneficial characteristics.

Multiscale Methods in Computational Fluid and Solid Mechanics

The basic idea of multiscale methods, namely the decomposition of a problem into a coarse scale and a fine scale, has in an intuitive manner been used in engineering for many decades, if not for centuries. Also in computational science, large-scale problems have been solved, and local data, for instance displacements, forces or velocities, have...

Mesh Association by Projection along Smoothed-Normal-Vector Fields: Association of Closed Manifolds

The necessity to associate two geometrically distinct meshes arises in many engineering applications. Current mesh-association algorithms are generally unsuitable for the high-order geometry representations associated with high-order finite-element discretizations. In the present work we therefore propose a mesh-association method for high-order...

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...

Numerical investigation of the membrane fluid-structure-interaction problem

A fluid-structure-interaction problem comprising a membrane interacting with an aerodynamic flow is of interest for research focused on the behavior of flexible aerospace structures. However, there are no systematic studies available in literature considering this type of problem. The present work examines the numerical solution method and the...

Interface-GMRES(R) Acceleration of Subiteration for Fluid-Structure-Interaction Problems

Subiteration forms the basic iterative method for solving the aggregated equations in fluid-structure-interaction problems, in which the fluid and structure equations are solved alternately subject to complementary partitions of the interface conditions. However, this subiteration process can be defective or inadequate, as it is endowed with...

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...