A biharmonic elliptic problem with dependence on the gradient and the Laplacian.
A C1-P2 finite element without nodal basis
A new finite element, which is continuously differentiable, but only piecewise quadratic polynomials on a type of uniform triangulations, is introduced. We construct a local basis which does not involve nodal values nor derivatives. Different from the traditional finite elements, we have to construct a special, averaging operator which is stable and preserves quadratic polynomials. We show the optimal order of approximation of the finite element in interpolation, and in solving the biharmonic...
A calculus for a class of finitely degenerate pseudodifferential operators
For a class of degenerate pseudodifferential operators, local parametrices are constructed. This is done in the framework of a pseudodifferential calculus upon adding conditions of trace and potential type, respectively, along the boundary on which the operators degenerate.
A comparison of some a posteriori error estimates for fourth order problems
A lot of papers and books analyze analytical a posteriori error estimates from the point of view of robustness, guaranteed upper bounds, global efficiency, etc. At the same time, adaptive finite element methods have acquired the principal position among algorithms for solving differential problems in many physical and technical applications. In this survey contribution, we present and compare, from the viewpoint of adaptive computation, several recently published error estimation procedures for...
A Conjugate Gradient Method and a Multigrid Algorithm for Morley' s Finite Element Approximation of the Biharmonic Equation.
A construction of a parametrix for an elliptic boundary value problem.
A construction of parametrices of elliptic boundary value problems
A fast solver for the first biharmonic boundary value problem.
A Legendre spectral collocation method for the biharmonic Dirichlet problem
A Legendre Spectral Collocation Method for the Biharmonic Dirichlet Problem
A Legendre spectral collocation method is presented for the solution of the biharmonic Dirichlet problem on a square. The solution and its Laplacian are approximated using the set of basis functions suggested by Shen, which are linear combinations of Legendre polynomials. A Schur complement approach is used to reduce the resulting linear system to one involving the approximation of the Laplacian of the solution on the two vertical sides of the square. The Schur complement system is solved by a...
A mixed finite element method close to the equilibrium model (Preliminary communication)
A mixed method for 4th order problems using linear finite elements
A mixed-Lagrange multiplier finite element method for the polyharmonic equation
A Multilevel Algorithm for the Biharmonic Problem.
A note on the Dirichlet problem for the elliptic linear operator in Sobolev spaces with weight
A Potential Method for the Biharmonic Equation.
A Quadratic Finite Element Method for solving Biharmonic Problems in IRn.
A representation formula for radially weighted biharmonic functions in the unit disc.
A supersolution-subsolution method for nonlinear biharmonic equations in
A symmetry result for a fourth order overdetermined boundary value problem.