A Legendre spectral‐Galerkin method for fourth‐order problems in cylindrical regions

Abstract A spectral‐Galerkin method based on Legendre‐Fourier approximation for fourth‐order problems in cylindrical regions is studied this paper. By the coordinate transformation, a three‐dimensional problem region transformed into sequence of decoupled with two dimensions and corresponding pole conditions are also derived. With appropriately constructed weighted Sobolev space, weak form established. Based form, discretization scheme proposed its error rigorously analyzed by defining new class projection operators. Then, set efficient basis functions used to write discrete as linear systems sparse matrix tensor product. Numerical examples presented show efficiency high‐accuracy developed method. Finally, an application Steklov numerical experiments once again confirm spectral accuracy