Finite Element Solution for Two Dimensional Laplace Equation with Dirichlet Boundary Conditions
Abstract
The steady state heat distribution in a plane region is modeled by two dimensional Laplace equation. In this paper Galerkin technique has been used to construct Finite Element model for two dimensional steady heat flow problem with Dirichlet boundary conditions in a rectangular domain. Results are then compared with analytic solution to check the accuracy of the developed scheme.References
Oakley, P.; Projects with people: the Practice of Participation in Rural Development, International Labor Organization, Geneva, (1991).
Rudqvist, Anders and Prudence WoodfordBerger; Evaluation and Participation: Some Lessons, SIDA Studies in Evaluation 96/1, SIDA Stockholm: SIDA, (1996).
Karl, M.; Monitoring and evaluating stakeholder participation in agriculture and rural development projects: a literature review, (2000) accessed 12th June 2009 at http://www.fao.org/sd/Ppdirect/Ppre0074.htm.
Mansuri, G. and V. Rao; Evaluating community- based and community driven development: a critical review of the evidence, Research Group, The World Bank, (2003) accessed 2nd February 2007 at http://siteresources.worldbank.org/INTECARE GTOPCOMDRIDEV/Resources/DECstudy.pdf
Goetz, A. and Gaventa, J.; Bringing citizen voice and client focus into service delivery, IDS working paper, No. 138, Institute of Development Studies, England (2001).
Blackburn, J. and C. de Toma; Scaling-down as the Key to Scaling-up? The Role of Participatory Municipal Planning in Bolivia’s Law of Popular Participation, in: Blackburn J. and J. Holland (eds) Who Changes? Institutionalizing Participation in Development, Intermediate Technology Publications, London, (1998).
Bhatnagar, B. and Williams, A. C.; Participatory Development and the World Bank: Potential Directions for Change, World Bank Discussion Paper vol.183, The World Bank, Washington, (1992).
Uphoff, N.; Monitoring and Evaluating Popular Participation in World Bank-Assisted Projects, in: Bhuvan Bhatnagar and Aubrey C. Williams (eds) Participatory Development and the World Bank: Potential Directions for Change, World Bank Discussion Paper vol.183, The World Bank, Washington, (1992).
Hoddinott, J., Adato, M., Besley, T., Haddad, L.; Participation and poverty reduction: issues, theory, and new evidence from South Africa, FCND discussion paper, No. 98, International Food Policy Research Institute, Washington, (2001).
Narayan, D.; The contribution of people’s participation: evidence from 121 rural water supply projects, environmentally sustainable development occasional paper series, No. 1, The World Bank, Washington, (1995).
Katz, Travis and Jennifer Sara; Making rural water supply sustainable: recommendations from a global study transport, water, and urban development, Water and Sanitation Department, United Nations Development Program- World Bank water and sanitation program, The World Bank, Washington D.C, (1997).
Isham, Jonathan and Satu Kahkonen; What determines the effectiveness of communitybased water projects? Evidence from Central Java, Indonesia on demand responsiveness, service rules, and social capital, Social capital initiative working paper, No. 14, The World Bank, Washington, (1999a).
Isham, Jonathan and Satu Kahkonen; Institutional determinants of the impact of community-based water services: evidence from Srilanka and India, Working paper, No. 236, IRIS Center, The University of Maryland, (1999b).
Ninan, K. N.; An assessment of European-aided watershed development projects in India from the prospective of poverty reduction and the poor, CDR working paper, No. 98.3, CDR, Copenhagen, (1998).
Kleemeier, Elizabeth; The impact of participation on sustainability: an analysis of the Malawi rural piped scheme program, World Development, 28(5) (may), (2000) 929- 944.
Cleaver, Frances; Paradoxes of participation: questioning participatory approaches to development, Journal of International Development, 11(4), (1999) 597-612.
Mosse, David; Colonial and contemporary ideologies of community management: the case of tank irrigation development in South India, Modern Asian Studies, 33(2), (1997) 303-338.
Ashiq, M.; Sampling Techniques: A Ready Reference for Social Scientists, Punjab Economic Research Institute, Lahore, (1980).
Chohan, A.; Role of Citizen Community Boards for local development under Punjab Local Government Ordinance 2001, Pakistan, 43rd ISOCARP Congress, (2007).
NRB (1999) official site accessed 12th December 2007 at: http://www.nrb.gov.pk/local_government/com munity_empowerment.htm
World population foundation Pakistan (1998- 99), accessed 29th July 2010 at http://www.wpfpak.org/html/gbv_project_locat ion.html.
Bureau of Statistics; Multiple indicator cluster survey, Punjab 2007-08, Planning and Development department, Government of Punjab, (2007-08).
NRB (1999) official site accessed 12th December 2007 at: http://www.nrb.gov.pk/local_government/figur e_2.gif?NOCACHE=1
Latif, M.; The politics of participation: evidence from five districts in Pakistan, Open Society Institute, Budapest-Hungary, (2005/2006).
ADB, DFID, World Bank; Devolution in Pakistan Annex 1, 2nd Vol.- Recent History, ADB, DFID, World Bank (2004).
CIET; National Reconstruction Bureau base line survey 2002 National report: social audit of governance and delivery of public services, CIET, Islamabad, (2002).
Shakil, M. A., Abu Talib, Noraini; Decentralization initiatives, economic and community development in Pakistan, International Journal of Trade, Economics and Finance, 1(4), (2010b) 380-386.
Shakil, M. A., Abu Talib, Noraini; Improvement of project sustainability by community participation: a case of Abbottabad district in Pakistan, African Journal of Business Management, 4(17), (2010a) 3761- 3768.
Paracha, S. A.; Devolution plan in Pakistan: context, implementation and issues, Open Society Institute, Budapest-Hungary, (2003).
DTCE; Annual progress report: helping devolution deliver, DTCE, Islamabad, (2006).
Ali, S.M.; Future of CCBs in Pakistan, Daily Times, 06 May, Pakistan(2006) accessed 16 January 2008 at http://www.dailytimes.com.pk/default.asp?page =2006%5C05%5C02%5Cstory_2-5- 2006_pg3_4
Daftary, D.; Elected leaders, community and development: evidence on distribution and agency from a case in India, Journal of Development Studies, 46(10), (2010) 1692- 1707.
Rahman, M. A., Sakano,T., and komai; Breaking Breaking the Vicious Circle of Distrust and Underdevelopment: The case of Pakistan, 41st ISoCaRP Congress, (2005).
