Convergence and Stability of Discrete Exterior Calculus for the Hodge Laplace Problem in Two Dimensions
By: Chengbin Zhu , Snorre H. Christiansen , Kaibo Hu and more
Potential Business Impact:
Makes computer math problems more accurate.
We prove convergence and stability of the discrete exterior calculus (DEC) solutions for the Hodge-Laplace problems in two dimensions for families of meshes that are non-degenerate Delaunay and shape regular. We do this by relating the DEC solutions to the lowest order finite element exterior calculus (FEEC) solutions. A Poincar\'e inequality and a discrete inf-sup condition for DEC are part of this proof. We also prove that under appropriate geometric conditions on the mesh the DEC and FEEC norms are equivalent. Only one side of the norm equivalence is needed for proving stability and convergence and this allows us to relax the conditions on the meshes.
Similar Papers
A Framework for Analysis of DEC Approximations to Hodge-Laplacian Problems using Generalized Whitney Forms
Numerical Analysis
Makes computer math problems solve more accurately.
Porous Convection in the Discrete Exterior Calculus with Geometric Multigrid
Computational Engineering, Finance, and Science
Solves hard math problems faster on computers.
Ghost stabilisation for cut finite element exterior calculus
Numerical Analysis
Makes computer models work with tricky shapes.