Optimal Isoparametric Finite Elements and Error Estimates for Domains Involving Curved Boundaries

1986/06/01 by M. Lenoir · 12 citations
Engineering · Computer Science · #Advanced Numerical Methods in Computational Mathematics #Numerical methods in engineering #Advanced Mathematical Modeling in Engineering

paper · doi:10.1137/0723036

Abstract

We describe a practical procedure for the triangulation of arbitrary n-dimensional regular bounded domains by isoparametric simplicial elements preserving the optimal order of accuracy. Along similar lines we prove general error estimates for the finite element solution of second order elliptic problems. Various kinds of nonhomogeneous boundary conditions can be dealt with, such as Dirichlet, Neumann and Robin boundary conditions.

Citations

• Mixed finite elements in ?3

Cited by

• High-order finite element method for perfect conductivity and linear elasticity with nearly touching inclusions
• Wavenumber-explicit stability and preasymptotic error analysis of UPML finite element method for obstacle scattering problems
• Discretely entropy stable weight-adjusted discontinuous Galerkin methods on curvilinear meshes
• A divergence-free parametric finite element method for 3D Stokes equations on curved domains
• Numerical analysis of the high-frequency Helmholtz equation using semiclassical analysis
• A Bernstein-Bezier Sufficient Condition for Invertibility of Polynomial Mapping Functions
• Penalty method with P1/P1 finite element approximation for the Stokes equations under slip boundary condition
• Well-posedness of a Pulsed Electric Field Model in Biological Media and its Finite Element Approximation
• A comparative study of finite element methods for a class of harmonic map heat flow problems
• Trace Finite Element Methods for PDEs on Surfaces
• The Hu-Zhang element for linear elasticity on curved domains
• Efficient entropy stable Gauss collocation methods

Related

• Optimal L^∞-error estimate for isoparametric finite element method in a smooth domain
• Isoparametric finite element analysis of a generalized Robin boundary value problem on curved domains
• Optimal simplex finite-element approximations of arbitrary order in curved domains circumventing the isoparametric technique
• Methods of arbitrary optimal order with tetrahedral finite-element meshes forming polyhedral approximations of curved domains
• Optimal-rate Lagrange and Hermite finite elements for Dirichlet problems in curved domains with straight-edged triangles