Mathematical Sciences: Finite Element Methods for           Constrained and Ill-Posed Variational Problems
{'Code': '03040100', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Michael Steuerwalt', 'PO_EMAI': None, 'PO_PHON': None}
This project involves continued research on finite element methods          for constrained and ill-posed variational problems. This includes               research on a new mixed finite element method for the equations of              anisotropic elasticity developed by the investigator and Professor              Douglas Arnold of the University of Maryland. The focus is mainly on the        computational effectivness of the method for pure traction and mixed            boundary conditions. The investigator has developed some a priori error         estimates for this difficult problem and now wants to check the                 effectiveness of the method on a computer for various choices of                boundary conditions. The most likely procedure that will be followed is         a simplified variational equation which reduces to a system of linear           algebraic equations with a positive definite matrix. To solve the system        efficiently, a preconditioned conjugate gradient method will be used.           Another project to be pursued involves finite element methods for the           first order scalar hyperbolic problem. The proposed research consists of        continued investigations on the use of nonconforming finite elements of         order higher than one (piecewise polynomials which are continuous at the        midpoints of triangles) including the derivation of a priori error              estimates and computational verification. The ideas of this research            will also be applied to the problem of identifying unknown functional           coefficients in a parabolic system of partial differential equations.           The work on this problem is relevant to underground oil reservoir               identification.                                                                     This research falls into the general area of numerical analysis and         computational mathematics. Its ultimate goal is to develop efficient            computational methods to be used in scientific problems involving               spatially distributed masses, energies, stresses and flows.
{'FirstName': 'Richard', 'LastName': 'Falk', 'PI_MID_INIT': 'S', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Richard S Falk', 'EmailAddress': 'falk@math.rutgers.edu', 'NSF_ID': '000162431', 'StartDate': '06/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Rutgers University New Brunswick', 'CityName': 'NEW BRUNSWICK', 'ZipCode': '089018559', 'PhoneNumber': '8489320150', 'StreetAddress': '3 RUTGERS PLZ', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'New Jersey', 'StateCode': 'NJ', 'CONGRESSDISTRICT': '12', 'CONGRESS_DISTRICT_ORG': 'NJ12', 'ORG_UEI_NUM': 'M1LVPE5GLSD9', 'ORG_LGL_BUS_NAME': 'RUTGERS, THE STATE UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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[{'Code': '1266', 'Text': 'APPLIED MATHEMATICS'}, {'Code': '1271', 'Text': 'COMPUTATIONAL MATHEMATICS'}]
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