A finite element method for second order nonvariational elliptic problems

Lakkis, Omar and Pryer, Tristan (2011) A finite element method for second order nonvariational elliptic problems. SIAM Journal on Scientific Computing, 33 (2). pp. 786-801. ISSN 1064-8275

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Abstract

We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence) form of a second order linear elliptic problem. The key tools are an appropriate concept of “finite element Hessian” and a Schur com- plement approach to solving the resulting linear algebra problem. The method is illustrated with computational experiments on three linear and one quasi-linear PDE, all in nonvariational form.

Item Type: Article
Keywords: Galerkin method, Galerkin approximation, Hessian recovery, scond order elliptic partial differential equation, nonvariational problem, finite element method, computational method
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
Depositing User: Omar Lakkis
Date Deposited: 19 Sep 2013 08:26
Last Modified: 10 Mar 2017 15:41
URI: http://sro.sussex.ac.uk/id/eprint/46362

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