The finite cell method with least squares stabilized Nitsche boundary conditions
Karl Larsson, Stefan Kollmannsberger, E. Rank, Mats G. Larson
Abstract
We apply the recently developed least squares stabilized symmetric Nitsche method for enforcement of Dirichlet boundary conditions to the finite cell method. The least squares stabilized Nitsche method in combination with finite cell stabilization leads to a symmetric positive definite stiffness matrix and relies only on elementwise stabilization, which does not lead to additional fill in. We prove a priori error estimates and bounds on the condition numbers.
Topics & Concepts
MathematicsFinite element methodLeast-squares function approximationA priori and a posterioriBoundary (topology)Boundary value problemApplied mathematicsPositive-definite matrixMathematical analysisStiffnessDirichlet boundary conditionDirichlet distributionMatrix (chemical analysis)Eigenvalues and eigenvectorsStructural engineeringStatisticsMaterials scienceEngineeringPhysicsEpistemologyPhilosophyEstimatorComposite materialQuantum mechanicsAdvanced Numerical Methods in Computational MathematicsAdvanced Mathematical Modeling in EngineeringDifferential Equations and Numerical Methods