Arterial walls in the healthy physiological regime are characterized by quasi-incompressible, anisotropic, hyperelastic material behavior. Polyconvex material functions representing such materials typically incorporate a penalty function to account for the incompressibility. Unfortunately, the penalty will affect the conditioning of the stiffness matrices. For high penalty parameters, the perfo...

Abstract. This paper provides a theoretical foundation for interior penalty discontinuous Galerkin methods for second order elliptic equations on very general polygonal or polyhedral meshes. The mesh can be composed of any polygons or polyhedra which satisfies certain shape regularity conditions characterized in a recent paper by two of the authors in [18]. The usual H conforming finite element...

We show that the weakly over-penalized symmetric interior penalty (WOPSIP) method has high intrinsic parallelism. Consider the following model problem: Find u ∈ H 0 (Ω) such that a(u, v) = ∫ Ω fv dx ∀ v ∈ H 0 (Ω), where Ω ⊂ R is a bounded polygonal domain, f ∈ L2(Ω), and a(w, v) = ∫ Ω ∇w · ∇v dx. This problem can be solved by the weakly over-penalized symmetric interior penalty (WOPSIP) method ...

We consider the fictitious domain method with H1-penalty for a parabolic problem. First, the sharp error estimate for the H1penalty problem approximating the original problem is derived. Then, we present some regularity analysis and prior estimate to the H1-penalty problem. The finite element approximation is investigated for discrete problems of two types, “continuous-time” and “single-step ba...