Convergence behavior of 3D finite elements for Neo‐Hookean material

On Multigrid Convergence for Quadratic Finite Elements

Quadratic and higher order finite elements are interesting candidates for the numerical solution of (elliptic) partial differential equations (PDEs) due to their improved approximation properties in comparison to linear approaches. While the systems of equations that arise from the discretisation of the underlying PDEs are often solved by iterative schemes like preconditioned Krylow-space metho...

Convergence rates for adaptive finite elements

In this article we prove that it is possible to construct, using newestvertex bisection, meshes that equidistribute the error in H-norm, whenever the function to approximate can be decomposed as a sum of a regular part plus a singular part with singularities around a finite number of points. This decomposition is usual in regularity results of Partial Differential Equations (PDE). As a conseque...

Data-driven finite elements for geometry and material design Citation

Crafting the behavior of a deformable object is difficult—whether it is a biomechanically accurate character model or a new multimaterial 3D printable design. Getting it right requires constant iteration, performed either manually or driven by an automated system. Unfortunately, previous algorithms for accelerating three-dimensional finite element analysis of elastic objects suffer from expensi...

Composite Finite Elements for 3D Image Based Computing

We present an algorithmical concept for modeling and simulation with partial differential equations (PDEs) in image based computing where the computational geometry is defined through previously segmented image data. Such problems occur in applications from biology and medicine where the underlying image data has been acquired through e. g. computed tomography (CT), magnetic resonance imaging (...

Convergence of finite elements enriched with mesh-less methods