A continuous/discontinuous Galerkin method for the biharmonic problem on surfaces
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We present a continuous/discontinuous Galerkin method for approximating solutions to a fourth order elliptic PDE on a surface embedded in R3. A priori error estimates, taking both the approximation of the surface andthe approximation of surface differential operators into account, are proven in a discrete energy norm and in L2-norm. This can be seen as an extension of the formalism and method originally used in [Dzi88] for approximatingsolutions to the Laplace-Beltrami problem. Using a polyhedral approximation Σh of an implicitly defined surface Σ embedded in R3 we employ continuous piecewise quadratic finite elements to approximate solutions to the biharmonic equation on Σ. Numerical examples on the sphere and on the torus confirm the convergence rate implied by our estimates.
IdentifiersURN: urn:nbn:se:umu:diva-79207OAI: oai:DiVA.org:umu-79207DiVA: diva2:640280