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## NUM METH IN DIFF EQUA

by: Evert Christiansen

22

0

1

# NUM METH IN DIFF EQUA MATH 610

Evert Christiansen
Texas A&M
GPA 3.92

Staff

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COURSE
PROF.
Staff
TYPE
Study Guide
PAGES
1
WORDS
KARMA
50 ?

## Popular in Mathematics (M)

This 1 page Study Guide was uploaded by Evert Christiansen on Wednesday October 21, 2015. The Study Guide belongs to MATH 610 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 22 views. For similar materials see /class/226056/math-610-texas-a-m-university in Mathematics (M) at Texas A&M University.

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Date Created: 10/21/15
MATH 610 Numerical Methods for PDEs Test 2 Thursday March 27 2008 Test 2 will be based on the material on boundary value problems for elliptic problems covered in class The following subjects will be included I Boundary value problem for PDEs of second order 1 Derivation of the variational formulation bilinear and linear forms7 abstract framework7 functional spaces coercivity7 continuity and various inequalities for the norms in L2Q7 HMS7 and L26 2 2 Finite element approximation by Ritz Galerkin method7 construction of nodal basis functions and computing the local mass77 and stiffness matrices this includes various nite elements treated as triplets 73973E7 where 739 is the geometric gure triangle or rectangle7 73 is the nite dimensional space of polynomials over 739 and E are the degrees of freedom77 or parameters that characterize the space The concept of unisolvency 3 Homogeneous area7 barycentric coordinates and application to computing element mass77 and stiffness7 matrices 4 Assembly of the global Ritz Galerkin system and incorporating the essential boundary conditions ll Error estimates of the nite element method 1 Optimal error estimates in a Hl norm energy norm b LZ norm using Nitsche trick 2 First and Second Strang7s Lemmas in abstract setting 3 Using Strang7s Lemmas for error estimates for second order elliptic problems when using various approximation procedures a veri cation of the conditions b error estimate due to numerical quadratures7 interpolation etc c nonconformity of the nite element space

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